The weapon has a x2 critical multiplier (unless he has certain other abilities), so he would:
roll 2d10 for the base weapon damage,
add his normal static damage bonuses (from strength, enhancement, etc) twice,
roll his variable bonuses (from flaming, frost, etc) once,
then roll an additional 3d10 (the extra base weapon dice from Greater Vital Strike) and
then add an additional +12 for Devastating Strike (+2 for each extra base weapon damage granted by Greater vital strike, x2 for the critical multiplier).
Since the critical roll has already been confirmed, Improved Devastating Strike's bonus has already been considered and does nothing for the damage roll.
The final calculation is: 5d10+12+(double the static bonuses)+(single instance of variable bonuses)
Yes to the x3 calculation.
For both the regular and unchained eidolon, the slam evolution grants a base damage of 2d8 for a huge creature.
Improved Damage bumps each 1d8 to 2d6 for a total of 4d6.
Improved Natural Attack bumps each 2d6 to 3d6 for a total of 6d6 base damage
Improved Vital Strike, which of course overrides its prerequisite of Vital Strike, deals three times the normal base damage for 18d6.
Bleed damage is calculated each round on the affected creature's turn, so is not rolled for as part of the attack's damage
The Energy Attacks evolution adds 1d6 of the chosen energy to the attack.
Final Calculation: 18d6 (slam damage) +1d6 (fire) + (static bonuses) and another 1d6 (bleed) at the beginning of all of the affected creatures turns until it stops the bleeding. Hope you brought your cube of d6's to the game.
The 3d8->4d8 progression is for attacks starting with a base of 1d10. There's generally a lot of confusion around this point, so I can't say I'm definitely right, but a search of these boards, the pertinent reddit forms, enworld, etc., leads me to believe that my answer mirrors the consensus.
Oh jeebus... I just found This FAQ and now I'm not so sure about this.
Specifically
Size Changes, Effective Size Changes, and Damage Dice Progression: I'm confused by how to increase and decrease manufactured and natural weapon damage dice when the weapon's size or effective size changes. There's a bunch of different charts, and I'm not sure which to use.
When the damage dealt by a creature’s weapons or natural attacks changes due to a change in its size (or the size of its weapon), use the following rules to determine the new damage.
• If the size increases by one step, look up the original damage on the chart and increase the damage by two steps. If the initial size is Small or lower (or is treated as Small or lower) or the initial damage is 1d6 or less, instead increase the damage by one step.
• If the size decreases by one step, look up the original damage on the chart and decrease the damage by two steps. If the initial size is Medium or lower (or is treated as Medium or lower) or the initial damage is 1d8 or less, instead decrease the damage by one step.
• If the exact number of original dice is not found on this chart, apply the following before adjusting the damage dice. If the damage is a number of d6, find the next lowest number of d6 on the chart and use that number of d8 as the original damage value (for example, 10d6 would instead be treated as 8d8). If the damage is a number of d8, find the next highest number of d8 on the chart and use that number of d6 as the original damage value (for example, 5d8 would instead be treated as 6d6). Once you have the new damage value, adjust by the number of steps noted above.
• If the die type is not referenced on this chart, apply the following rules before adjusting the damage dice. 2d4 counts as 1d8 on the chart, 3d4 counts as 2d6 on the chart, and so on for higher numbers of d4. 1d12 counts as 2d6 on the chart, and so on for higher numbers of d12.
• Finally, 2d10 increases to 4d8 and decreases to 2d8, regardless of the initial size, and so on for higher numbers of d10.
Damage Dice Progression Chart
1
1d2
1d3
1d4
1d6
1d8
1d10
2d6
2d8
3d6
3d8
4d6
4d8
6d6
6d8
8d6
8d8
12d6
12d8
16d6
Which does indeed put the base weapon damage at 4d8 as GMS said.
But then there's
Size increases and effective size increases: How does damage work if I have various effects that change my actual size, my effective size, and my damage dice?
As per the rules on size changes, size changes do not stack, so if you have multiple size changing effects (for instance an effect that increases your size by one step and another that increases your size by two steps), only the largest applies. The same is true of effective size increases (which includes “deal damage as if they were one size category larger than they actually are,” “your damage die type increases by one step,” and similar language). They don’t stack with each other, just take the biggest one. However, you can have one of each and they do work together (for example, enlarge person increasing your actual size to Large and a bashing shield increasing your shield’s effective size by two steps, for a total of 2d6 damage).
Which sounds like the Improved Natural Attack feat and Improved Damage evolution don't stack (which drops the base damage back to 3d8).
So, because FAQ, I guess the final total is 9d8 (+1d6 fire and 1d6 of bleed on their turn)
