Does a grease spell affect where the caster is standing, or the caster in general when cast on itself? I've read of some rules about AOE spells not affecting the point of origin or something... but would like to know RAW
Yes, a Grease spell targeted so that the caster is included in its AoE will affect the target. Grease affects every creature within an area, making no exception for its caster:
When the grease appears, each creature standing in its area must succeed on a Dexterity saving throw or fall prone.
Spells with an AoE of cube, cone, or line do not affect their point of origin, but Grease is not any of those.