I did 2 hours of research to find the answer to this bizarre question. If you look at it on the surface it seems obvious, get lucky to find 15 scrolls of upgrade, and apply it to a greataxe +3, to get a +18 which deals 23-153 damage. Spoiler alert this is not the greatest amount of damage possible, far from it.
If you don't care about EVERYTHING you need to deal the most damage, then just look at this amount possible 1112.9 damage!!!!!
First off you can get a +19 greataxe if you reforge them at the troll blacksmith. An axe that's at least +3 (upgraded from scrolls or planning to upgrade axe) and a an axe that is any tier (not upgraded from scrolls). It will add a +1 to the greataxe, making the best upgraded one a +19. So 159 damage.
Whetstones can balance weapons and armor, so balance it for damage, you will deal 1.5x more damage. Now it's 238.5 damage.
Assassins can deal 1.6x more damage if they are invisible for long enough. Up the damage to 381.6 damage.
Here are some minor damage buffs, 20 strength when the greataxe has a weight of 15, sucker punch tier II is 2+ damage, ring of force +2 deals 3 extra damage, and ring of might +2 is 3 extra strength (so +3 damage). After all of that you can deal up to 400 damage.
Lastly debuffs, doomed makes enemies take double damage, and vulnerable makes enemies take 33% more damage. Making the highest possible damage 1070.4, or if you have 10 potions of Adrenaline Surge at the same time, then the final damage outputs maximum amount being that final number of 1112.9!
If you know anything else to increase damage, or something that is wrong in this forum post let me know.
Btw the most damage I ever did was 273 damage to an evil eye. (+10 greataxe, with assassin class)