Ordinary Abnormality

this ability switches one stat at random (attack, def, hp, luck) with your enemies - but I can’t tell what it factors in and what it doesn’t. does it factor in artifacts, abilities, shrine buffs?

Nope.

can you stack it? if so, does that switch 2 stats randomly?

It does stack, but the stats are rolled randomly; if you get the same stat twice, the second activation is negated.