Oddity XP System
The Oddity XP System is an alternative experience system introduced in version 0.1.10.0.
The main purpose of this system is to allow players to level at a similar rate regardless of what their build and play-style is. Going through the world stealthily, guns blazing (or in some cases diplomatically) or anything in between should now earn you similar amount of experience.
Since version 0.1.11.0, completing quests also awards experience in Oddity XP system.
Oddity items
These items are scattered throughout Underrail, mostly at points of interest. Some of them are gained by killing critters and other specific types of enemies, but since each oddity item can be studied a limited number of times, you can only farm XP from a single creature type to a certain point.
Also, there are generally more instances of an oddity item type placed than you need, so you don't have to have 100% exploration score to get them all. Though, some of them will be unique and only awarded for discovering special areas or defeating bosses.
They can also be found when playing with Classic XP System, but do not have as big of a role in leveling process there. Compared to Oddity XP System, they award 50 times more experience in Classic XP System, where other experience gains are also much larger.
Oddity catalog
As of version beta 0.2.0.1, You can open the oddity catalog window O to review your character's oddity collection and see how many oddity types are still left to be found.