Invocations are class specific - in particular, they're not the same type of invocation. Dragonfire Adept invocations are "draconic invocations." From the class description:
A dragonfire adept has a repertoire of attacks, defenses, and other abilities known as draconic invocations, which allow her to focus the draconic energy that suffuses her soul. A dragonfire adept can use any invocation she knows at will.
The section on invocations later in the book then describes the ones intended for Dragonfire Adepts as "draconic invocations."
Similarly, the Warlock's class description (Complete Arcane, p. 5) says:
A list of available invocations can be found following this class description, and a complete description of each invocation can be found in Chapter 4 of this book
...implying that invocations found elsewhere in the rules aren't available to Warlocks unless they specifically say they are.
However, all is not lost! Wizards published the Infernal Adept feat in an online article, which allows Dragonfire Adepts to learn Warlock invocations and vice versa:
Prerequisites: Ability to use greater invocations as a dragonfire adept or a warlock, special
Benefits: You learn one invocation from another class's list, choosing an invocation no more than two grades lower than the highest grade of invocation you know. For instance, an 11th-level warlock could learn a least invocation from the dragonfire adept list, while a 16th level dragonfire adept could learn a least or lesser invocation from the warlock list.
The default for any invoker class is to be unable to choose any invocation except those explicitly assigned to it. Complete Arcane, Complete Mage, and Dragon Magic all explicitly assign various invocations to the warlock class. Complete Mage does not, however, include greatreach blast or spellblast in the list of invocations it assigns to the warlock, nor does it assign those invocations to the warlock separately when they are described within prestige class abilities. As such, those invocations are not available to a warlock unless or until he gains the class feature that offers them.
To see this, let’s start with the very definition of warlock invocations:
Invocations: [...] A list of available invocations can be found following this class description, and a complete description of each invocation can be found in Chapter 4 of this book.
(Complete Arcane pg. 7)
The warlock can literally learn only those invocations that are listed in its description there. At no point in the entire column-and-change description of the invocations ability does the warlock gain any ability to gain any other invocation; the class feature only enables the selection of those invocations listed within the class description itself.
That doesn’t mean that these are the only invocations a warlock can ever take, however! D&D 3.5e is an exception-based ruleset, which means future material can, and does, make exceptions to earlier rules. That isn’t the point. The point is that the default state for any given invocation is for it to be not an option for a warlock. Something has to make it an option for a warlock in order for it to become one.
And the books consistently do exactly that when introducing new invocations. For example,
Also included are over twenty new invocations for the warlock class found in the Complete Arcane supplement. These invocations are governed by the rules in that book.
(Complete Mage pg. 89)
That quote is from the beginning of Chapter 4, Spells and Invocations, of Complete Mage. It specifies that these new invocations are for the warlock class. That provides an exception to the rule on page 7 of Complete Arcane that says a warlock’s options are only those invocations included right there on pages 8 through 10 of Complete Arcane.
Not listed in Chapter 4, however, are spellblast or greatreach blast. Those invocations are described only in the descriptions of the relevant prestige classes—and those descriptions only give them to those prestige classes, rather than make them available to just any warlock. (In fact, the word “warlock” does not appear in the description of either class feature.)
For another example, consider Dragon Magic, which presents the dragonfire adept class, another invoker. These quotes are the references to its invocations:
Invocations: [...] See Draconic Invocations, below, for a list of available invocations.
(Dragon Magic pg. 25)
Draconic Invocations
Each draconic invocation falls into one of four grades: least, lesser, greater, or dark. These invocations are described briefly below. See Chapter 3: Draconic Magic for full descriptions.
(Dragon Magic pg. 26)
The invocations available to dragonfire adepts (see page 24) are described in this section. The format for invocation descriptions is given below, followed by the lists of invocations available to dragonfire adepts.
(Dragon Magic pg. 78)
Note that none of these make any mention of the warlock class, and yet they are presenting “invocations,” and specifically, invocations graded into four tiers of least, lesser, greater, and dark. The invocation format does not include an associated class, as the spell format does, either, and the dragonfire adept reprints several invocations that Complete Arcane and Complete Mage had made available to the warlock, under this heading that says they’re available to dragonfire adepts as well.
And as perhaps the final nail in the coffin, Dragon Magic also presents several new warlock invocations. There are in an entirely different section, which reads
Because the powers of warlocks (see Complete Arcane) are tied to their dark nature, they're usually incompatible with draconic magic. However, warlocks living in a world where dragons are more active learn to tune their powers toward the destruction of such foes. These new invocations are intended for use by warlocks who expect to face dragons (or similarly formidable spellcasting opponents) in combat.
(Dragon Magic pg. 81)
Note again the complete lack of anything here saying that dragonfire adepts cannot take these new warlock invocations; per Dragon Magic pg. 25, there is no reason to do so because these invocations do not appear in the list that begins on page 25, so they are unavailable to dragonfire adepts by default.
We have an existing Q&A about dragonfire adepts and warlocks and whether they can take each other’s invocations—and it comes to the same conclusion as this answer, that invocations are class-specific and can only be taken by a dragonfire adept or warlock if they are printed in a section assigning the invocations there to that class.
So yes, there is something preventing regular warlocks from taking those invocations: those invocations are simply never made available to them unless or until they gain the class feature from the relevant prestige class that makes them available.
Best Answer
With no Flaws, and moderate cheese
This version does not assume any variants from Unearthed Arcana are in play (though fractional saves get mentioned because this variant simply makes much more sense—it does not affect viability here). The cheese level is relatively low considering the goal, entering a prestige class “only” one level early. Though ur-priest is arguably cheesy no matter what you do with it...
Human Warlock 1, Precocious Apprentice and Invisible Spell
This gets you an arcane caster level, least invocations, a 2nd-level arcane spell, and a metamagic feat. It also gets you a Will save of +2 (and ½, if you are reasonable and use fractional saves), and you should put 4 ranks in Intimidate.
Precocious Apprentice is from Complete Arcane, in a sidebar on page 181 rather than in the feats chapter. Some argue that it cannot qualify for prestige classes that require “ability to cast 2nd-level arcane spells,” usually on the grounds that you have only one. But so does a Sorcerer 4, and no one’s denying them entry on those grounds.
Invisible Spell is from Cityscape. Really, any metamagic feat works here, I chose this one primarily because it doesn’t change the spell level. This means you can use it on your Precocious Apprentice spell.
Furthermore, Complete Arcane has this gem:
As far as the Sudden feats are concerned, this rule is solid. But Sudden feats are not the only metamagic feats that don’t require modified spell slots (for instance, Insivible Spell), and the wording here implies that this is a general truth about how metamagic works with spell-likes. RAW, this clause doesn’t have the authority to make that statement about the general case, and it’s the only reference in the rules to this idea. That makes it pretty invalid, strictly speaking. However, it is a pretty neat idea that helps out a relatively weak class, so consider allowing it. It would mean you could use Invisible Spell on invocations. Consider eldritch glaive for slicing people up with no apparent motion on your part.
You might alternatively consider Extend Spell for eventual Divine Metamagic shenanigans.
Warlock 1/Binder 1
This gets you 1st-level vestiges. It also bumps your base Will up to +4 (+5 if using fractional).
Warlock 1/Binder 1/Duskblade 1, Improved Binding
Duskblade has a good Fortitude save, bringing it up to +2 (or, if being reasonable and using fractional saves, +3⅙). Honestly, literally any good-Fort class would work here. I chose duskblade because it’s thematic, it gets Will too, arcane attunement is solid enough, and it has its own arcane caster level, which will be relevant in a bit.
Duskblade is from Player’s Handbook II.
Improved Binding means you qualify as a 3rd-level binder for vestiges’ sake, which means 2nd-level vestiges. Between this and Precocious Apprentice, you now qualify for...
Warlock 1/Binder 1/Duskblade 1/Anima Mage 3, Spell Focus (evil)
You have a 2nd-level arcane spell, you have 2nd-level vestiges, and you have “any metamagic feat” and 4 ranks in Intimidate. So you qualify for and can take levels in anima mage. Anima mage can progress warlock just fine, for all that warlock has some difficulty entering. Three levels brings you to 6th overall, with 4th-level warlock invoking and 4th-level binder pact-making.
Anima mage is from Tome of Magic.
You also have +9 as a base Will save (+11 if using fractional; less sane, but skipping the additional +2 each time you take a new class with a good save is typical and appropriate, even though Unearthed Arcana does not do this—that would give you a far more reasonable +5), and +3 base Fort save (+4⅓ with fractional). By taking Spell Focus (evil), you qualify for...
Warlock 1/Binder 1/Duskblade 1/Anima Mage 3/Ur-priest 2
Ur-priest is an exceptionally appropriate class here: it’s evil, it’s all about stealing power you shouldn’t have, and it gets 9th-level spells in as many levels. Two levels gets you 2nd-level divine spells and Rebuke Undead.
Ur-priest is from Complete Divine.
Warlock 1/Binder 1/Duskblade 1/Anima Mage 3/Ur-priest 2/Eldritch Disciple 8
Eldritch disciple advances invocations, and except at 1st, divine spellcasting. After 8 levels of it, you’ll cast spells as a 9th-level ur-priest, enough to get 9th-level spells.
You’ll also have the invocations of a 12th-level warlock, i.e. greater.
We could have done this with mystic theurge instead of eldritch disciple, saving us a level but costing us any and all class features. Eldritch disciple’s class features are mediocre, but they’re better than nothing, and things work out so that this doesn’t really cost us anything.
Eldritch disciple is from Complete Mage.
Warlock 1/Binder 1/Duskblade 1/Anima Mage 7/Ur-priest 2/Eldritch Disciple 8
Another four levels of anima mage bring binding up to 8th level, enough for two vestiges of up to 5th level (thanks to Improved Binding). It also brings warlock invoking to 16th, exactly what we need to hit the dark invocations.
Conclusion
We have 9th-level divine spells off the cleric spell list, dark invocations off the warlock list, and a pair of 5th-level vestiges off the binder list. We used the 1st, 3rd, and 6th level feats, as well as the human bonus feat, but the rest are available, for instance to grab Shape Soulmeld and Open Chakra feats, or by getting into Divine Metamagic.
With Flaws, and extreme cheese
Unearthed Arcana’s flaws allow a character to gain an additional two feats at 1st level, in exchange for said flaws. This is extremely useful here.
Anima mage is also amenable to extreme levels of early entry shenanigans. As in, 2nd level entry shenanigans.
Warlock 1/Anima Mage 10/Ur-priest 2/Mystic Theurge 7
The two feats from flaws can be Bind Vestige and Improved Bind Vestige from Tome of Magic. This gives us the ability to bind a single vestige, which grants only a single power, as a 5th-level binder, i.e. up to 3rd-level vestiges. That allows us to eliminate the level of binder altogether.
Thus, entry into Warlock 1/Anima Mage is entirely possible, and absurdly, it advances us as if we were taking binder levels even though we have none to begin with. Since we no longer have a level to burn at 3rd (we used to because we needed to wait until 3rd to get Improved Binding), we’ll skip duskblade and delay ur-priest until 9th or 10th (depending on the use of fractional).
We can, of course, take Improved Binding once we get into anima mage. If retraining or psychic reformation is available, our Warlock 1/Anima Mage 2 can take Improved Binding and safely ditch Bind Vestige and Improved Bind Vestige.
I also switch to mystic theurge because it allows us to complete anima mage entirely, so we get vestige casting, i.e. the ability to cast a spell as if Still and Silent and as an immediate action (!). Once per day, but who cares, that’s incredible. Eldritch disciple’s got nothing on that.
We end up with the invoking of an 18th-level warlock (dark invocations), the spellcasting of a 9th-level ur-priest (9th-level divine spells), and the pact-making of a 10th-level binder (a pair of 6th-level vestiges assuming you take Improved Binding).
Conclusion
Hitting 6th-level vestiges is a big deal. That means you get Zceryll, the Star Spawn, which is hands-down the most powerful vestige in print (assuming you allow it at all, which you might consider not doing). For whatever reason, the 6th level of vestiges is also oddly crowded, with nine entries (second only to 4th level, which has ten). There are only seven total vestiges that you don’t get, and only four of those are in Tome of Magic.
Including a bit of other things
We do still have four feats (six, in the second case and using psychic reformation to undo Bind Vestige and Improved Bind Vestige). That’s enough to do a few things.
Meldshaping
If we are azurin instead of human, we still get a bonus feat, but instead of the bonus skill points we get a single point of essentia. Take Shape Soulmeld, Bonus Essentia, and some other [Incarnum] feat—they each give one essentia—and you’ll be able to shape one soulmeld and max out its capacity (which is based on character level). You also have room for at least one more feat, for Open Least Chakra, Open Lesser Chakra, or Open Greater Chakra, depending on where you want to bind this soulmeld.
If using flaws and psychic reformation, Expanded Soulmeld Capacity (or an incarnum focus) and another [Incarnum] feat lets you fill your souldmeld with five essentia. Getting to six is possible using Expanded Soulmeld Capacity and an incarnum focus, but you can only fill that through more psychic reformation cheese to get another [Incarnum] feat.
Sublime Way
Tome of Battle maneuvers are inherently easy to tack onto any character. You get half your level to your Initiator Level, can take Martial Study up to three times, and Martial Stance as much as you want (but since you can only use one stance at a time, you wouldn’t want more than one anyway). That’s four feats, if you choose to use them that way.
On the other hand, your BAB will be atrocious, and most of the maneuvers of the Sublime Way involve attacks or improve attacks, so those are not especially useful to you. Still, there are some excellent options:
Shadow jaunt or shadow stride – teleportation is useful to anyone, and move-action teleportation, in the latter case, is actually unavailable to you from all your spellcasting. Shadow stride would only be available by using your 18th-level feat on Martial Study, however.
Distracting ember – swift-action is easy, and if you have a rogue in the party, free flanking is nice.
Mountain hammer – great for breaking into or out of places, since it can go through walls, doors, locks, and so on. Note however that objects tend to have a fair amount of HP as well as hardness, so this may still be slow-going unless you invest in some damage improvements.
Counter charge, Setting Sun throw maneuvers – these don’t require BAB too much, since they work like trip attacks that can use Strength or Dexterity. Depends a lot on whether or not you have much of those. Note that Small size can be an advantage with these, however.
Iron heart surge – completely remove anything... kinda. Talk to your DM about what exactly it can and cannot end. Do not use the Customer Service answer; it’s terrible.
White Raven tactics – completely broken if you can use it on yourself, and arguably overpowered even if you can’t. Still, it’s a great maneuver, and getting it through Martial Study eliminates most of the big problems.
Step of the wind, child of shadow, hunter’s sense, bolstering voice, leading the charge, absolute steel stance, dance of the spider, roots of the mountain, leaping dragon stance, shifting stance, step of the dancing moth, press the advantage – all stances that are useful to you. Pick one that you like best.