barbarian/warlock - can it be done?

[Mukade]

I'm currently playing a barbarian by the name of Hektor Aloyisius Burnisde the Fourth. 6 and a half feet of muscle, Hektor was always helpful on the Burnside farm, even if his skin was the colour of onyx and the consistency of granite, his eyes glowed a dull orange and small fires would sometimes spontaneously start in his vicinity.
On his 18th birthday, his parents Mary-Anne and Hektor the Third Aloyisius Burnside, told Hektor that, to nobody's surprise but his own, he was not their natural born son. He's not a smart man. Rather, they had found him in a cracked open egg shaped chunk of volcanic rock while travelling in another land. Why, they had even saved a chunk of the rock to give to him on this fateful day. Hektor fashioned a maul from this chunk of rock and, taking that and the lessons in kindness and manners his adoptive family had given him over the years, set off to find his birth parents.

Mechanically, Hektor is a Scourge Aasimar Storm Soul (desert) Barbarian, level 5

Unbeknownst to him, Hektor's birth parent is a storm giant quintessent who spends most of it's time as a semi conscious storm formed by the continuous pyroclastic eruption of a volcano. When Hektor eventually meets his birth parent, he'll hopefully establish a positive if confusing relationship, where he may swear fealty and become his semi-divine sire's agent in the mortal world as a reskinned fiend warlock.
This is partly because spells like hellish rebuke, fire shield and green (orange) flame blade mesh so well with Hektor's characterisation, but the fact that you can't cast spells while raging makes me wonder if this could be an effective combo. I know that at level 14 as a Storm Soul barbarian you get a fire-shield like retributive strike ability, but is barbarian/warlock (barblock? warbarian?) a feasible option?
What's the solution here? Is there a way to cast or concentrate on spells while raging? Roleplay it as character development, Hektor relying more on calmly using what his demigod volcano mama gave him, until he really needs to get mad and break out a 10' swathe of fiery destruction? Take pact of the blade & eldritch smite, which I believe you can use while raging, for a limited option big hit?
I'm currently thinking, theoretically, to go barbarian 14/warlock 6, which may not be the most powerful character but would certainly fit the character's themes.
What do you think, playgrounders?

[BloodSnake'sCha]

RAW you can and can't concentrate on a spell while raging but this is because the rules are written poorly.
It will probably won't help you unless your DM is like me and love the stupid RAW stuff.

You can still cast spells with no concentration like Armor of Agathys and fire shield.

Eldritch Smite is nice and good especially when you can reckless and look for criticals to use it effectively.

The fiend THP work really well with your resistances.

It is nice, I still think that the level 20 barbarian feature is great but if you want to multiclass then multiclass.

[CTurbo]

If it fits your character story/theme I say go for it. My Monk took 3 levels of Fiend Warlock because it made sense story wise even if it was a poor choice from a powergaming standpoint. Story always wins over mechanics for me.

Even still, Barbarians are always raging and there is no reason why you could make ANY class work with Barbarian, even Wizard. Barbs are always kinda of one dimensional anyway so multiclassing with any caster immediately boosts their overall impact on the party.

I've also taken 2 levels of Bard with one of my Barbarians because it made so much sense to the character.

[Swaoeaeieu]

It is homebrew, but a while back i found these: multiclassing feats. (https://www.reddit.com/r/UnearthedArcana/comments/5qcfey/multiclass_enabling_feats/?utm_source=amp&utm_medium=&utm_content=post_body)
One of them is a feat that lets barbarians cast spells, but they have to make constitution checks for every spell or lose the spellslot.
Maybe your DM will allow it?

[CheddarChampion]

That backstory is a lot to take in.
Personally I prefer Zariel tiefling or fallen aasimar for stats on a barbarian.
I think you'll want a final split of barbarian 4/warlock 16 - maximum ASI's.

Edit: oh, you already have 5 barbarian levels.
Yes, warlock can work, but you'd want warlock levels from here on out.
I suppose you'll want celestial pact for that backstory, which let's you heal even in a rage and eventually gives THP for the whole party.
The Armor of Agathys spell is good, as mentioned.
Blade pact would be good for improved pact weapon and lifedrinker.
Might as well get GWM if you're already a barbarian with a maul.

For a scourge aasimar start with 14/12/14/10/10/16. Keep boosting Str as you level up. Go pact of the blade for extra attack + lifedrinker.

Celestial warlock for self healing + THP for party would be good.
Fiend warlock for THP on kill + resistance to one damage type would be good.
Bear totem barbarian for resistances would be good, zealot for flavor, or ancestral guardian for tanking would be good.

Personally I'd go with Zealot 1/Fiend 5/Zealot +3/Fiend X.
Zariel tiefling 16/12/14/8/8/16.
Grab PAM, boost Str, then boost Cha.
Cast armor of agathys then rage.
Embrace the bloodshed.
Evil campaigns only.