The key is in looking at the card text.
If a card becomes "unaffected" by other effects, this means any effect that would affect the card in question, not effects or conditions that would apply to other cards or players.
Threatening Roar, Dimension Gate, etc do not affect specific monsters. Waboku does, but it affects your monsters, not the opponent's. An opponent's Omega could not use its effect to be immune to Waboku and kill one of your monsters by battle, because Waboku is not affecting that Omega.
Messenger of peace is vice versa. It does affect Constellars, so Omega can get around this.
Thanks to danna45 for the above.
Alduin: I actually see your point of view and am no longer annoyed at you.
[1/31/2014 12:11:00 AM] Armand: i listen to deadman even when he's rude. it helps that he's not rude for the sake of it, but rather, he is just a bit, when necesarry (1/31/2014 12:11:16 AM) Erosion: That's because he's Saxton Hale himself (1/31/2014 12:12:17 AM) Vincent: So what, Deadman became DeadManlyMan? (1/31/2014 12:13:09 AM) Erosion: Basically, he's gotten so good at making insightful posts, he could go off on a drunken rant on how x is bad and y is good, but nobody will mind because he's damn good at what he does (1/31/2014 12:14:01 AM) Vincent: Well yeah, and that's who he is; he just feels the need to fight for what he believes in as hard as he is capable of, and he is capable of a lot.