Black Mage, Two Knights, and a Thief; Classic.
Thing about Omega is I kinda need to abuse Firaga to even start to deal with the wave cannons.
There's 2 methods I recommend for this one.
1: Put a Reflect Ring on your Black Mage, Thief, and 1 of your Knights. Have the other Knight with Hermes Sandals, Diamond Helmet, and Aegis Shield. Have Black Mage reflect Thundagas off your party while the others serve as Heal bots. Have Wonder Wand queued up to use Shell so you can reduce the damage from Thundaga on the Knight even further. The non-Hermes Sandal'd Knight and Thief can be Zombied to make this easier(Less healing items to use and health to watch), just make sure to unequip their weapons.
2: Zombie all 3 of Non-Black Mages while they have a Reflect Ring on, and give your Black Mage Hermes Sandals, Sages Surplice, and a Thunder/Magus Rod. Same as the previous strat, queue up Shell and put it on your Black Mage, to help reduce a lot of the damage they may take. Keep an eye on your HP when doing this and only reflect Thundaga off your party when you are certain you'll be alive when your next turn comes up so you can heal.
Bring plenty of Hi Potions and Elixirs for both strats.
I more recommend Strategy 2 since I've had more success with that one than one. It's not a fun strategy, but it's your best bet for surviving Omega.
For Shinryu, put your party into Critical HP, except 1 Knight, use Wonder Wand to cast Berserk on Shinryu, and have your Non-Critical Knight use Guard to negate all the physical damage from Shinryu. Have fun murdering him after that.