If you don't want to lose Odin, or have a higher chance to make him appear, look here.

To not lose Odin: If you don't want to lose Odin, then do NOT go to the island from where you encounter him. If you do, at the point when you fight Seifer, he will use a skill which goes along these lines: Zantetsuken reverse. This will kill Odin (despite the fact that he's so powerful, he doesn't really need to die). Gilgamesh is horrible. He has 4 weapons (which everybody knows) which includes the Excalibur and the Excalipoor (a fake which does a measley 1 damage to all your opponents).

To have a higher chance to make him appear: Turn on the Analog option on your controller (unless you don't have it) and make one stick go up, the other go down. Keep switching, but this must be done when a monster is encountered.

Hope that helps.