So I spent a bit of time messing around with Overdose mode on a new character, a Golem Predator. Here are some observations so far:
The 20x experience bonus seems to be applied across the board just about everywhere. Anything that modifies EXP gets that bonus. This includes pets, random NPCs and enemies. Hilarity ensues when the common bats you fight start to level their greater evasion, and even level up from it. On the plus side, I was able to get Poppy out of the cave by more or less letting him go on a supervised training montage until he was a bit less fragile.
Of note, things that DECREASE exp also get boosted. So if you do manage to get cocky and die, expect to lose several points in your stats at once. Not that it's too hard to get them back, but still...
This increase is also applied after all other modifiers are taken into effect. So anything that gives skill exp will give at least 0.020 to a skill. With just a bit of patience (less than normal Elona requires, surely), you can effectively ignore potential. Probably for the best, too, since the skills level up so fast there's no way to keep it at a reasonable level.
Bonus skill points almost feel like cheating... At any decent amount of potential, one point = one skill level, basically.