Question about Initiate of the Draconic Mysteries

[DeadAggressor]

I took 7 levels of monk and have Superior Unarmed Strike, Monk's Belt, and Monk's Tattoo. I also have Fanged Ring and a continuous effect Great Mighty Wallop CL 8. So my damage is currently 8d8. If I took 4 or even 8 levels of IoDM, would the die increases increase it to 8d10 and 8d12 respectfully or 12d8 and 16d8?

[HunterColt22]

I took 7 levels of monk and have Superior Unarmed Strike, Monk's Belt, and Monk's Tattoo. I also have Fanged Ring and a continuous effect Great Mighty Wallop CL 8. So my damage is currently 8d8. If I took 4 or even 8 levels of IoDM, would the die increases increase it to 8d10 and 8d12 respectfully or 12d8 and 16d8?

It increases the size you get to use, not the number of dice you get to jingle.

[hex0]

Be sure to take Improved Natual Attack and Superior Unarmed Strike as well.

[Biffoniacus_Furiou]

You can apply your own effects in the most beneficial order, so always add on Greater Mighty Wallop first as it can only take your effective size to colossal.

You have an effective level of Monk 20 for unarmed damage, for a Medium base of 2d10.
Going up one size to large size makes it 4d8, and extrapolating the size increase chart (http://www.d20srd.org/srd/equipment/weapons.htm) for weapon damage would probably convert that to double the Bastard Sword progression. Greater Mighty Wallop at CL 8 would make that 6d8 at Huge size. If you can improve this then you definitely should, as it can take you up to Colossal and then you can further increase the effective size beyond that.
The Fanged Ring gives you Improved Natural Attack for one more size, so effectively Gargantuan at 8d8.

Initiate of the Draconic Mysteries would eventually give you yet two more size increases, exceeding Colossal by one step. Further extrapolation of the damage chart for a Bastard Sword from Large and up would probably go as follows:
2d8, 3d8, 4d8, 6d8 is given. That's 2d8, 3d8, 4d8 is twice what's two steps before it, 6d8 is twice what's two steps before it. This is further solidified by the Greatsword damage progression, which follows double-two-steps-before for one additional step.
Colossal+1 would be 8d8, Colossal+2 would be 12d8, Colossal +3 is 16d8, Colossal+4 is 24d8, Colossal+5 is 32d8, Colossal+6 is 48d8, etc. Note that's for a Bastard Sword base damage, Monk 20 is double those numbers.

So with all of that and a Caster Level 20 Greater Mighty Wallop, you would have the following:
Medium, base 2d10.
Greater Mighty Wallop CL 20, effectively Colossal at 12d8.
Fanged Ring for Improved Natural Attack, effectively Colossal+1 at 16d8.
Initiate of the Draconic Mysteries for two sizes, effectively Colossal+3 at 32d8.

Get a (Permanency) Enlarge Person for an actual size increase (the effects of which can be applied after effective size increases) for Colossal+4, which is 48d8.
Replace that with an augmented Expansion psionic power for Colossal+5, 64d8.
Replace that with a Giant Size spell (CA) via a greater Ring of Spell Storing for Colossal+7, 128d8.