Start with 1 level of Fighter

As a melee spellcaster you need good AC and Con save for concentration, a single-class Warlock has neither.
That one level of Fighter will give you Two-Weapon Fighting and better armor until you reach acceptable Dex.

Str: 8
Dex: 15
Con: 14 (13+1)
Int: 10
Wis: 12
Cha: 16 (14+2)

The Charisma could be lower, as Hex is your bread and butter, but there is no better place for the points. At the first chance, get Resilient(Dex), for an even Dex score, and better saves.

Every level indicator is for character level, so subtract 1 for Warlock level.

Feats/ASI

Nothing raises DPR like an increase in your attack stat, it is about 15-20%.

L5: Resilient(Dex)
L9: +2 Dex
L13: +2 Dex
L17: Dual Wielder¹
L20: Warcaster or Sentinel

Equipment

Pick up two Short Swords, and the largest Medium armor, as you do not have the Strength for Heavy.

Invocations

L3: Fiendish Vigor
L3: Agonizing Blast²
L6: Thirsting Blade
L8: Devil's Sight?³
L10: Armor of Shadows⁴
L13: Lifedrinker

Spells

By the level you take it

Cantrips:
L2: Eldritch Blast
L2: Green-Flame Blade (or Booming Blade, if you find very generous or stupid GMs)
L5: Frostbite, Sword Burst or Thunderclap, great when you would have Disadvantage on attacks
L11: Lightning Lure

Spells known:⁵
L2: Hex
L2: Hellish Rebuke
L3: Dissononant Whispers⁶
L4: Invisibility
L5: Hold Person
L6: Fear
L7: Fly
L8: Evard’s black tentacles⁷
L9: Banishment
L10: Telekinesis
L12: Counterspell

Further multiclassing

As a Warlock, you reach 90% of your full potential on level 12 in my opinion. You will never get any spell slots above 5th, and Mystic Arcanum is very far behind what full spellcasters get. You just got Lifedrinker and an ASI, time to change.

Rogue
Up to 9 levels. You will use Finesse weapons anyway, preferably next to one of your colleagues, so Sneak Attack is a simple DPR increase. Swashbuckler is good for Initiative, Assassin for critical, and Arcane Trickster gives new spells known.

Fighter
3 more levels. Battlemaster is great, but you can get some nice things out of Eldritch Knight as well.

Bard
Up to 9 levels. Lore Bards are awesome, both spells and Bardic Inspiration are great.

Sorcerer Up to 9 levels. Metamagic is good, you can convert unused spell slots to Sorcery Points before short rests. Use them for Twinned Dissonant Whispers, or Quicened Hold Person for two critical attack from your Action.

Full Build

L1: Fighter for AC and Con save and Fighting Style
L2-L6: Warlock for Hex, Invocations, ASI and Extra Attack
L7: Bard for extra spells and cantrips and Inspiration
L8-L14: Warlock for Entropic Ward, Evard’s black tentacles, Banishment and Lifedrinker
L15+: Bard for more frequent Inspiration

1) Dual Wielder is popular and cool, but it is strictly worse than +2 Dex, as it provides about half the DPR increase. AC increase is the same, damage increase marginally better than an ASI, but +2 Dex also improves your attack. And your Initiative, and your save, and your Stealth.
Only take DW if you can not increase your attack stat, so once it is maxed out, or on 1st level as a Variant Human.

2) Agonizing Blast makes your backup ranged option viable.

3) You could take Devil's Sight earlier, it is popular with Darkness, but it is very party unfriendly, and I find it overrated. I would take it for a human, but you have Darkvision anyway.

4) Improves AC by one once you have 20 Dex.

5) As you do not increase your Charisma, I focus on spells that are not based on it, like Fly, Invisibilty, or Hex. Otherwise, I go for multi-target spells, so at least some of the them fails the save.
Take single target spells that you could upcast for more targets (Hold Person, Banishment) when you can already upcast them, or on the level right before.

6) Dissonant Whispers does not fit the criteria from 5), but is great anyway. Can target virtually everything, does some damage on a save too, and provokes Opportunity Attacks.

7) Arguably the best controlling spell in the game, and not even Sorcerers get it, so use it proudly!
Does damage, provides Advantage, imposes Disadvantage. Getting out takes an ability check, so no one is proficient, similarly, Magic Resistance only applies to the initial save. If an enemy manages to get out, you can push it back in.

Yes, but you have to be level 12 to do this

The Sage Advice articles says:

You can also use Pact of the Blade to bond with a magic weapon, turning it into your pact weapon. This magic weapon doesn’t have to be a melee weapon, so you could use the feature on a +1 longbow, for instance

This takes care of the ranged pact weapon, and allows the use of both Thirsting Blade and Lifedrinker with a ranged weapon. This means you can attack twice with your Attack action using a magic ranged weapon.

And the Sage Advice compendium says:

Does Crossbow Expert let you fire a hand crossbow and then fire it again as a bonus action? It does! Take a look at the feat’s third benefit. It says you can attack with a hand crossbow as a bonus action when you use the Attack action to attack with a one-handed weapon. A hand crossbow is a one-handed weapon, so it can, indeed, be used for both attacks, assuming you have a hand free to load the hand crossbow between the two attacks.

This allows you to attack twice -- once with your action, another with your bonus action. Since you have Thirsting Blade (which works with any weapon as long as it's your pact weapon), you can get three attacks in all.

However, while Thirsting Blade is available at 5th level, Lifedrinker is available at 12th level. So to complete this build, you have to be a 12th level character at minimum. Most of it, you can enjoy from 5th level onwards though, as only Lifedrinker is the high level component.