How do you get omega shenron on dbz budokai 3?

First you have to beat the GT Saga in story mode, then he'll randomly be summoned when you gather the Dragon Balls.

What you do is once you have the Dragon Balls, save your game. Then summon the Dragon, and if you don't get the one you want, wish for stuff anyway but don't save. When you get back to the main menu, load your save game and try again
Which dragon shows up is completely random. But if you want to make sure you get the one you want, save right before you summon the dragon. If green shenron or porunga come out just reset your PS2 and summon the dragon again. Keep doing this until you get the one you want.