I'm going to go out on a limb and say that the Omega Beams might not affect Etrigan the same because of his mystical makeup (if they affect him at all).
Etrigan has crazy strength feats and his demon flame is killer. He stalemated Lobo over a few issues back in the day.
Darkseid has taken Supes' best punches and kept going. He's not just Omega Beams and an army.
The Omega Beams don't have to erase every being they fight... nor can they. That doesn't mean they can't hurt powerful beings.
And they certainly can and will hurt Etrigan. Which even if they can't put him down, that only sets up another blast, a punch, kick, or a triple backflip uppercut.