Has there been anything that explains thus far if characters and the overlord level up during the campaign?

They not level up in common way we are used from RPGs. They just recieve XP points after each finished dungeon and they can spend these XP for new skill cards. Thats all

Yeah, there aren't "levels" as such. The system has more in common with skill-based RPGs like World of Darkness, where characters improve their skill set by spending XP on specific things, rather that earning enough XP to hit a pre-defined limit and just gaining stuff at that point.

A hero's (or OL's) overall power level would be tracked by how much XP he has earned in total. That can be tracked on paper throughout the game, or calculated by adding up the XP costs of all the cards he has already, plus any unspent XP he's still holding on to.