Another Sorlock Build... with a few ways to do it...

https://rpgbot.net/dnd5/characters/classes/wizard/subclasses/evoker/
https://rpgbot.net/dnd5/characters/spells/magic-missile/
https://www.sageadvice.eu/scorching-ray-dd-errata/

According to Jeremy Crawford back in 2015, this bonus applies to each missile of magic missile and to all targets of an AOE, but only to one attack for multi-attack spells like Scorching Ray. If Empowered Evocation applies to each missile, Magic Missile becomes very powerful. This conflicts with Crawford’s more recent rulings, where he has ruled that each missile from Magic Missile is a separate damage roll, so similar damage bonuses only get applied to one of the missiles. Personally I think the more-recent ruling makes more sense, but discuss it with your DM. For the magic missile case, see our Practical Guide to Magic Missile.

https://www.reddit.com/r/3d6/comments/qf9iki/wizsorlock_and_magic_missile_a_guide_to_making/

This is better now with 6 Draconic Sorcerer.. 6 Celestial Warlock

Magic Missile
You create three glowing darts of magical force. Each dart hits a creature of your choice that you can see within range. A dart deals 1d4 + 1 force damage to its target. The darts all strike simultaneously, and you can direct them to hit one creature or several.

At higher levels: When you cast this spell using a spell slot of 2nd level or higher, the spell creates one more dart for each slot above 1st.

Since Magic Missile only rolls damage once and you multiply that damage by the number of bolts, it works well with spells and features that add damage to single dice/damage rolls. Plus, it's a guaranteed hit with no chance of a saving throw.

We're going to use metamagic to change Magic Missile's damage type to fire (or possibly another) using Transmuted Spell:

Transmuted Spell. Cost: 1 Sorcery Point
When you cast a spell that deals a type of damage from the following list, you can change that damage type to one of the other listed types: acid, cold, fire, lightning, poison, and thunder.

Draconic Sorcerer:

Elemental Affinity
Starting at 6th level, when you cast a spell that deals damage of the type associated with your draconic ancestry, you can add your Charisma modifier to one damage roll of that spell. At the same time, you can spend 1 sorcery point to gain resistance to that damage type for 1 hour.

Celestial Warlock:

Radiant Soul
Starting at 6th level, your link to the Celestial allows you to serve as a conduit for radiant energy. You have resistance to radiant damage, and when you cast a spell that deals radiant or fire damage, you can add your Charisma modifier to one radiant or fire damage roll of that spell against one of its targets.

[or]

1 Hexblade...

Pact Choice

I like Pact of the Tome (with Book of Ancient Secrets) or Pact of the Chain.

What's interesting about Book of Secrets is taht it allows you to learn any Ritual spell (regardless of class) as long as you can satisfy the level requirements. This means we'll have access to level 3 rituals at level 6.

The Hexblade gets online at first level thanks to Hexblade's Curse:

Hexblade's Curse
You gain a bonus to damage rolls against the cursed target. The bonus equals your proficiency bonus.

Your proficency bonus scales with your character level, not your warlock level, so this will always be relevant. It won't match your CHA modifier (assuming it's 5) until level 13 but you get partial bonuses as you level.

https://worldbuildersjunction.com/what-is-proficiency-bonus-in-dd-5e-how-it-works-calculated/

The nice thing about going Hexblade here (among a lot of other things) is that it doesn't lock you into fire damage. You can chose acid, lightning, fire, or lightning.

Monster Resistance Count: Cold (~230) > Fire (~200) > Lightning (~150) > Acid (~75)

https://blackcitadelrpg.com/elemental-adept-feat-5e/

https://forums.giantitp.com/showthread.php?379165-MM-Resistances-Immunities-Vulnerabilities-and-Damage

Why would we want to go 6 into warlock?

Pact of the Chain works better here...

This might not work...

https://forums.giantitp.com/showthread.php?500098-Bestow-Curse-and-Magic-Missile

Scorching Ray, though?

Sign of Ill Omen
You can cast bestow curse once using a warlock spell slot. You can’t do so again until you finish a long rest.

There's a fair amount of utility for Bestow Curse but we're going to focus on the last bullet point:

Bestow Curse
While the target is Cursed, your attacks and Spells deal an extra 1d8 necrotic damage to the target.

I'm not in love with the eplan of having to be in Touch range of the target, but Pact of the Chain's familiar helps out with that.

Eldritch Blast, with Hex, can be a replacement for Magic Missile.

You can use metamagic on cantrips, so you're free to give yourself the bonuses from Elemental Affinity and Radiant Soul.

Magic Items that Push This Further

https://rpg.stackexchange.com/questions/193443/are-there-any-game-features-that-allow-a-wizard-to-add-damage-to-every-spell-cas

Honorable Mention: Imbued Wood Focus (+1 to damage rolls) and Chromatic Dragon-Touched Focus (Rare - 1d6 to damage rolls with acid, cold, fire, lightning, or poison)

http://dnd5e.wikidot.com/wondrous-items:imbued-wood-focus

Ioun Stone of Mastery

Tome of Leadership and Influence (increase CHA past 20)

Star Card (Deck of Many Things) - https://www.dndbeyond.com/magic-items/4617-deck-of-many-things

What doesn't work? A Goblin's Fury of the Small.

https://rpg.stackexchange.com/questions/105415/does-the-goblin-trait-fury-of-the-small-apply-to-each-hit-of-an-attack-or-spell

There are other features besides metamagic that can change the damage type without expending resources but most of the other tricks this build uses has limited resources anyways. We're not focused on sustained damage, we have Eldritch Blast and Hex for that -- this is for single (or dual) target burst damage.

https://rpg.stackexchange.com/questions/103617/can-your-familiar-concentrate-on-a-spell-it-delivers

https://www.belloflostsouls.net/2020/09/dd-magic-missile-mastery-how-to-explode-anyone.html

https://www.reddit.com/r/dndnext/comments/bc342g/magic_missile_build_572_damage_in_one_round/

https://blackcitadelrpg.com/shadow-magic-sorcerer-guide-5e/

https://blackcitadelrpg.com/metamagic-guide-5e/

https://blackcitadelrpg.com/spells/eldritch-blast-5e/

https://www.reddit.com/r/powergamermunchkin/comments/ag0weo/magic_missile_massacre/

https://www.reddit.com/r/3d6/comments/b7dcwc/the_deadeye_wandslinger_optimizing_damage_dealt/

Frequently Asked Questions (FAQ)

Will Magic Missile kill a PC outright if hit by multiple missiles?

It's unclear, but probably.

https://rpg.stackexchange.com/questions/73190/would-striking-someone-at-0-hit-points-with-an-entire-magic-missile-spell-automa

Arcane Firearm (Artillerist) with Evocation Wizard? It probably doesn't work (at least they wouldn't stack).

You can use your arcane firearm as a spellcasting focus for your artificer spells. When you cast an artificer spell through the firearm, roll a d8, and you gain a bonus to one of the spell's damage rolls equal to the number rolled.

Beginning at 10th level, you can add your Intelligence modifier (minimum of +1) to one damage roll of any wizard evocation spell that you cast.