I am a Half Orc Fighter (Battle Master) 4/Paladin (Oath of Conquest) 5, wielding a Greataxe (d12)
Using a wish, I have gained the Brute trait as it appears in the Gladiator from the Monster Manual:
A melee weapon deals one extra die of its damage when [it hits] – (MM 346)
So on a regular hit, 2d12.
Half Orcs have the trait Savage Attacks:
When you score a critical hit with a melee weapon attack, you can roll one of the weapon's damage dice one additional time and add it to the extra damage of the critical hit. – (PHB 41)
This is not doubled, it is a bonus die, for a total of 5d12 on crit, yes? Yes.
If I take the Orc Racial Feat Orcish Fury:
…When you hit with an attack using a simple or martial weapon, you can roll one of the weapon's damage dice an additional time and add it as extra damage of the weapon's damage type. Once you use this ability, you can't use it again until you finish a short or long rest…- (XGtE 74)
This Does get doubled, Yes?
As a Fighter (Battle Master) I could take Maneuvering Attack:
When you hit a creature with a weapon attack, you can expend one superiority die to [add it] to the attack's damage roll…(PHB 74)
This Does get doubled, Yes?
7d12 + 2d8
The Paladin's Divine Smite feature:
… when you hit a creature with a melee weapon attack, you can expend one paladin spell slot to deal radiant damage to the target, in addition to the weapon's damage. The extra damage is 2d8 for a 1st-level spell slot, plus 1d8 for each spell level higher than 1st, to a maximum of 5d8. – (PHB 85)
According to the above, this gets doubled as well? If I cast it at 2nd level,
7d12 + 2d8 + 6d8 radiant.
With Great Weapon Fighting Style:
When you roll a 1 or 2 on a damage die for an attack you make with a melee weapon that you are wielding with two hands, you can reroll the die and must use the new roll. The weapon must have the two-handed or versatile property for you to gain this benefit. – (PHB 84)
If the Critical Hit Rules allow doubling the dice of all these various sources of damage, because they are all part of the attack, I may then safely say I may reroll, at least once, any of these dice involved that result in a 1 or a 2, Yes?
My strength bonus is 5, and if I take the feat Great Weapon Master (PHB 167) I get -5 to the attack for +10 damage bonus.
7d12+2d8+15 plus 6d8 Radiant, rerolling the first results, at least on the d12s of 1 or 2.
Is this all correct?
Divine Smite says (emphasis mine):
This wording is a little ambiguous as to whether Smite is part of the attack damage or a damage modifier. Damage modifiers aren't doubled. However, Sage Advice says that Smite is part of the attack damage and crittable since it does not require a save or its own attack roll.
The rest looks correct so you'd have: Normal - 1d12 Slashing
Great Weapon Fighting (PHB p72) allows rerolls for an initial 1 or 2 on the d12 dice. The Radiant Damage and Superiority Die is in addition to weapon damage thus not covered by the GWF feature. (Sage Advice)