The celadrin should work…

The Dragon #350 article "Legacies of Ancient Empires" (50-7) by Eric Boyd describes the celadrin planetouched. They possess the type outsider and the subtype native, have Level Adjustment +1 and no racial Hit Dice, and possess, among other abilities, the racial trait elven blood:

For all special abilities and effects related to race, a celadrin is considered an elf. Celadrins, for example, can use elven weapons and magic items with racially specific elven powers as if they were elves. (52)

While this description of the racial trait elven blood is slightly different from the description found in the Player's Handbook and Monster Manual for Dungeons and Dragons 3.5, it nonetheless aligns perfectly (with appropriate finding-and-replacing, obviously) with the half-elf racial trait elven blood from the Player's Handbook for Dungeons and Dragons, Third Edition! Despite Dragon magazine having converted to 3.5e over forty issues earlier, with such evidence in hand, it should be a small matter to convince the DM to make a minor adjustment that will bring this outdated Third Edition description of the racial trait elven blood up to 3.5e standards.

…And so should the fey'ri…

The planetouched fey'ri (Races of Faerûn 118-21) possess the type outsider and the subtype native, have Level Adjustment +2 (or +3 with damage reduction or the spell-like ability dimension door or enervation) and no racial Hit Dice, and possess, among other abilities, the racial trait elven blood like the aforementioned celadrin and other pre-3.5 revision elflike creatures (hence making some minor adjustments by the DM a necessity).

The Player's Guide to Faerûn Web enhancement "Monster Update" mentions in passing that fey'ri are also tieflings (5). This allows a fey'ri to, for example, meet requirements and feat prerequisites it couldn't've met as just a planetouched fey'ri. That is, a generous DM may allow such a fey'ri to enter the class tiefling paragon (UA 45-6) (for all the good it'll do the fey'ri) or take a feat like Planetouched Animal Affinity (Races of Faerûn 167) (for all the good that feat does anyone).

(A player can ask the DM if this also means that a fey'ri gets, in addition to the typical traits of a fey'ri, the traits of the typical tiefling (Monster Manual 209-10). The DM will probably say No, but a player can ask, and, really, LA +2 is a lot. But, here, just in case, take this helmet, and look out for hurled dice.)

…but other creatures will struggle

While the Epic Level Handbook belabors the creature's closeness to elves, the leShay (202-3), an epic fey with 50 Hit Dice and no supplied Level Adjustment, has the natural ability elf traits that does not seem to enable a leShay to meet elven blood requirements and prerequisites, instead only providing the leShay with minor elf-like features without it actually being an elf. However, with a leShay's fifty fey racial Hit Dice, this DM would seriously consider a house rule granting a leShay the racial trait elven blood. At the typical point at which a leShay is usable as a PC, that's not going to be a big deal.

Keith Baker's Web article "Druids of Khorvaire, Part Four" includes the description of the Valenar warhorse, an animal with 4 Hit Dice, no supplied Level Adjustment, and an Intelligence score of 2 (and, according to Dungeon Master's Guide 172, the DM should not "allow players to play creatures who have an Intelligence score of 2 or lower"). Nonetheless, if the DM is accommodating (maybe the Valenar warhorse is the subject of an awaken effect?), the section Valenar Horses says

Aside from its enhanced speed and Dexterity, a Valenar horse can live for up to ten times the lifespan of a normal horse; the Tairnadal [elves] attribute this longevity to the elven blood they believe runs through the veins of the steed.

(Emphasis mine.) Ask the DM if this belief is true then, if it is, ask if it means a Valenar horse technically meets prerequisites and requirements as if the horse has the racial trait elven blood. (Were this DM to approve such a thing, he would concoct a tale that has an injured Valenar horse in the distant past receiving a field transfusion from his elven master. So you know.)

Note: I made a good faith effort to work my way through this edition's printed Wizards of the Coast material as well as Web material. I did not search extensively issues of Dragon, Dungeon, Living Greyhawk Journal, or Polyhedron nor third party material that bears the officially approved Wizards of the Coast seal. Other options may yet exist, buried in more obscure sources.

They can take any race-restricted character option

As pointed out in this answer, in Pathfinder, most half-breeds of humans are also treated members of both parent races, and thus, also treated as humans. This rule extends to:

• Half-orcs

Orc Blood: Half-orcs count as both humans and orcs for any effect related to race.

• Half-elves:

Elf Blood: Half-elves count as both elves and humans for any effect related to race.

• Aasimars with Scion of Humanity racial trait:

Scion of Humanity: Some aasimars’ heavenly ancestry is extremely distant. An aasimar with this racial trait counts as an outsider (native) and a humanoid (human) for any effect related to race, including feat prerequisites and spells that affect humanoids.

• Tieflings with Pass for Human racial trait:

Such a tiefling doesn’t need to succeed at a Disguise check to appear to be human and count as humanoid (human) as well as outsider (native) for all purposes (such as humanoid-affecting spells like charm person or enlarge person).

• Sylphs, Undines, Oreads and Ifrits with Mostly Human racial trait:

Such geniekin appear to be human, save perhaps minor features like unusual eye color, and they count as humanoid (human) as well as outsider (native) for all purposes (such as humanoid-affecting spells such as charm person or enlarge person).

• Fetchlings with the Bound to Here racial trait:

Fetchlings with this racial trait count as outsiders with the native subtype and humanoids with the human subtype for any effect related to race, including feat prerequisites and spells that affect humanoids.

• And any shapechanger (like: Kitsunes, Skinwalkers or Doppelgangers) that takes the Human Guise feat:

You count as both human and your race for the purpose of taking character options, such as archetypes, feats, spells, traits, and prestige classes.

Keep in mind that planar half-breeds exist for non-human races, as pointed out in Blood of Angels (Aasimars) and Blood of Fiends (Tiefling). Such variants would be an exception to this, as pointed out on the sidebar of Blood of Angels, for instance:

Non-human aasimars have the same statistics as human aasimars with the exception of size. Thus a halfling aasimar is Small but otherwise possesses the same statistics and abilities as a human aasimar-the difference is purely cosmetic. Non-human aasimars do not possess any of the racial abilities of their base race. However, they are usually raised in the same cultural context as other members of their base race, and thus generally adopt the same fighting style as their peers, use the same types of weapons and armor, and study the same skills.

So from a rules-as-written perspective, an Aasimar that has an elf parent and takes Scion of Humanity would count as humanoid(native) and still count also as humanoid(human) instead of humanoid(elf).

But are also affected by any race-specific effects

This may sound strong, but keep in mind that this also affects race-specific effects or effects based on creature type, like the Bane special weapon property, or an Intelligent Magic Item that wishes to defeat/slay all members of a specific race.

A half-orc, for example, is both a humanoid(orc) and a humanoid(human) creature. Meaning that they are affected by both a Human-Bane weapon and a Orc-Bane weapon (luckily, bane doesn't stack). A half-elf would meet the requirements of crafting a Cloak of Elvenkind. And so on.