This is only my assumptions so take it with the grain of salt but from what I understand:
Stage 1 can fight Stage 0.
Stage 1 and Stage 0 can fight Devil host/Devil's power user ( like DD ) but they can't beat them.
Arcane stage mage can harm Devils with everything coming from his arsenal.
Now the exceptions:
Luck being Stage 1 ( I think it was stated but I'm not sure. Talking about Gaja runes teachings ).
Luck beat Devil's power user which was impossible from his Stage standpoint.
Ceranos = Arcane stage attack.
Yuno is Stage 1.
Spirit Dive attacks = Arcane stage attacks.