That's not unpossible.To qualify for all those Multiclasses you would need standard Human. (14, 14, 14, 13, 13, 13)
Barbarian Unarmed Defense, Rage, Fighting Style - Dueling, Monk Martial Arts,Sneak Attack
Using a Shortsword, you can rage and deal 2d6+6, and then in subsequent turns deal another 1d4+4 unarmed attack.
And then you've got 6 spell slots and a crazy amount of prepared level spells, including a lot of reaction ones.
If I were going Barbarian/Wizard
Start as a Barbarian, proficiency in Constitution saves and medium armor. Martial weapons.
School of Abjuration, those temporary hitpoints become twice as good while raging.
Several spells do not require concentration:
Mirror Image, Animate Dead, False Life, Blink, Fire Shield, Mordenkainen's Hound, Tenser's Floating Disk
(Place the Hound on top of the Disk

)
The more I think about it, I've got a feeling the resistance to nearly all damage combined with constant Temporary hitpoint generation might make a DM lose his shlt.