Does the specific rule of using a magic item, which supplants you with the ability to cast a spell override the general rule of raging? Does the specific rule of eldritch invocations, such as fiendish vigor (you can cast the False life spell at will) override rage? Can a familiar, such as a warlocks imp(stated to make concentration checks in its stat block) make concentration checks while its master is raging?

"If a specific rule contradicts a general rule, the specific rule wins." 

I'm sure this is rules lawyering as most multiclass combinations were unimagined at the time of creation. But there are rules for multiclassing, and there are rules for overriding "general" rules. So here we are, any thoughts? I'm pretty sure there was no intention for (or against) these combinations, so that leaves RAW and Rules as Fun.

In terms of effect the actions (in combat) would layer,

Rage: remove the ability to cast spells

Use Magic Item: gain the ability to cast a single spell

Or 

Eldritch invocations are not considerd spells??? (Idk about this one) 

Rage: you cant cast "spells"

Invocation: WILL yourself the effects of False Life

Or

Cast Darkness on yourself though Familiar: Familiar Concentrates

Rage: you arent the one concentrating on the spell

Or 

Rage: YOU can not cast Spells

Familiar uses Item Action: gains the ability to Cast Darkness on Barbarian 

A barbarian's rage is not a "general rule". It is a specific rule which is overriding a general rule - that normally you are not prevented from casting spells while moving around.

So then you are in the case of how two specific rules interact.

Rage overrides everything else. You cannot cast spells of any kind whilst raging.

You can’t cast spells or concentrate on them while raging, this in any possible way, wether it's a class feature or magic items, if it says "cast x" you can't.

One thing you might be able to argue is an Artificer's spell-storing item, which says

While holding the object, a creature can take an action to produce the spell’s effect from it, using your spellcasting ability modifier.

Technically no casting there. But if it's a concentration spell it will still immediately end and a DM wold be within their rights to just say no anyway.

Quote from scatterbraind >>

One thing you might be able to argue is an Artificer's spell-storing item, which says

While holding the object, a creature can take an action to produce the spell’s effect from it, using your spellcasting ability modifier.

Technically no casting there. But if it's a concentration spell it will still immediately end and a DM wold be within their rights to just say no anyway.

Yeah it never mention "casting" afterall . 

Your familiar can't concentrate on a spell for you.

Quote from ChoirOfFire >>

Your familiar can't concentrate on a spell for you.

 But it can concentrate on it's own spell yes?

Quote from scatterbraind >>

One thing you might be able to argue is an Artificer's spell-storing item, which says

While holding the object, a creature can take an action to produce the spell’s effect from it, using your spellcasting ability modifier.

Technically no casting there. But if it's a concentration spell it will still immediately end and a DM wold be within their rights to just say no anyway.

 Interesting I knew there had to be some things, of note a few wands have effects rather than spells 

Quote from Zod_El >>

Quote from ChoirOfFire >>

Your familiar can't concentrate on a spell for you.

 But it can concentrate on it's own spell yes?

 Yeah, if your familiar gets a way to cast spells on its own then it can concentrate on them. As far as I know, the only way that can happen is with a magic item. I would be very hesitant as a DM to allow familiars to use any magic items, but your mileage may vary on that. At the very least, I think it's reasonable to say that your familiar would need hands and, depending on the spell, the ability to speak, so you're going to need to be a Warlock with a Pact of the Chain.

Quote from scatterbraind >>

One thing you might be able to argue is an Artificer's spell-storing item, which says

While holding the object, a creature can take an action to produce the spell’s effect from it, using your spellcasting ability modifier.

Technically no casting there. But if it's a concentration spell it will still immediately end and a DM wold be within their rights to just say no anyway.

 If this came up in a game of mine I think I'd rule that the barbarian could activate the stored spell, sort of as if they were activating a magic item. But not be able to concentrate on said spell if they're raging.