Okay, I think I know what the problem is, but I'll ask clarifying questions. Have you fought an enemy with the intention of winning through violence? Have you gotten any Exp that is displayed on the front page of the menu, not under status?
Okay, so you have the Chair next to Oracle in the base, correct? And you are able use it and enter, being able to move between the Red (Melee) Green (Survival) Yellow (Ranged) and purple (Psi) nodes?
(TBH I didn't win a fight, instead I was laying with the girls, till I was 12 hours in, but that is besides the point. )