If you are trying to beat Omega and Shinryu for bragging rights, use the strategies listed below;but please, if you want a challenge, don't use the strategies listed below, as they are VERY cheap ways of killing them that people use all the time.

Omega:
1. Using Spellblade Thundaga/!Sword Bolt3.
2. Using X-fight/!Sshot.
3. Casting Stop. (Though it only works if you Reflect it off one of your own characters, since Omega has Auto-Reflect)

Shinryu:
1. Using Dragon Lances.
2. Having all your characters Jump in addition to using the Dragon Lances.
3. Casting Berserk.

A VERY cheap glitch in the SNES/PS1 version:
- Using !Mix with a Maiden's Kiss and Holy Water, causing them both to be put into Berserk status no matter what their status immunities are.

Though what you should almost ALWAYS do is:

-Equip Fire Rings against Omega to absorb his Atom Ray attack.
-Equip Coral Rings against Shinryu to absorb his Tidal Wave attack.
-Set the battle time to "wait" (optional)

Good luck beating them.