Omega Weapon is the most powerful of the top-tier enemies. Let's not kid each other. However, he is not impossible. This method is expensive, and requires you to work from the beginning of the game, but is probably the most likely to work.
Step 1: GFs. Collect every GF you can. Even the hidden ones, from Siren when battling Gerogero on Disc 1, to Eden when facing Ultimate Weapon in Disc 3 or 4. You WILL need them ALL.
Step 2: Necessary Side-Quests. Defeat the CC Group, and complete the Chocobo Forest and Queen of Cards Quests. You'll probably need a lot of GF/People cards to do this. My faves for cards are Squall, Seifer, Edea, Rinoa, and Quistis, as this combo allows you to be prepared for any card an opponent may play. Lower levels can use Sacred, Minotaur, Zell(get from Zell's mom), and 2 others that are strong on up&right, and down&right. Make sure you play CC King until you have the Gilgamesh card, and CC Joker, who isn't necessary, should be played, as he has Leviathan(very good replacement for Squall[?]).
Step 3: Acquiring “stuff”. If you haven't already done so, get all of the RF abilities, for magic, items, and cards. Hook everyone up with ultimate weapons, and get your GFs at the highest level you can. Make sure they have boost.
Step 4: Group and Junctions... First and foremost, your Big Three had better be at level 100; they’re going to need everything they can get. If they aren’t, go to one of the Islands Closest to (insert realm of afterlife here), and battle. The best way is to have Quistis with low health and Initiative, so she can jump into battle, immediately get her Limit Break, use Degenerator or Bad Breath (whether you’re battling one enemy or two), and rack up the experience. This also levels your GFs. For the fighting group, my personal suggestion is Zell, Squall, and Quistis. Irvine is a good choice if you have to replace Quistis, but she is better, due to her typically higher magic stat. You should almost never use Selphie and Rinoa; Selphie’s Slot Limit is far to random and time consuming, Rinoa’s Limits aren’t that great either. Angel Wing means losing control of her, and only Wishing Star is any good for using Angelo; plus, the chance of it coming up is totally random.
Zell needs Cerberus, Pandemona, Cactaur, and Siren. Squall should have Bahamut and Tonberry, and Quistis NEEDS Eden, plus the highest compatibility possible, but compatibility is not a problem. I’ll explain why later. All the characters should have AbilityX4 with a GF, and one of the ExpendX# –1 abilities, just in case. From here, it’s about junctioning only the best. Ultima, Flare, Meteor, Death, Curaga, Regen (makes for a good junction), Full-Life, Aura, Pain, Reflect, Stop – anything you can find on the Islands Closest to (insert realm of afterlife here), and then some. You NEED 100 of all of them. Don’t waste time with any low-level magic, or useless stuff like Scan. Either RF it to higher magics, or dump it. Note that, as Omega is a boss, Diablos will not work on him; this is actually OK. Put Diablos on one of the 3 characters you won’t be using against Omega, and activate Enc-None, to speed things up.
Zell should have the set-up Attack, Magic, GF, and Recover (from Leviatian); for abilities, make sure he has Initiative. Squall will be the same, except Item instead of Recover. Quistis, or your choice of a third character, will have Attack, Magic, GF, and Revive (from Alexander). If you can afford it, I suppose you could have Mug on a character, but it’s not important, and I don’t think you can Mug anything good.
Step 5: Card Refining. You’ll need to refine one of the Brothers cards to gain the 10 Adamantine, so you can get the Lionheart for Squall (unless you were very, very lucky battling Adamantoise), Angelo(?) for the 100 LuvLuvGs, which are to up your compatibility with GFs (why I said not to worry), and 10 Holy Wars from the Gilgamesh card. These Holy Wars are the most important of all the CardRFs; I’ll explain why in a minute.
Step 6: Finding Omega… Omega is a real pain to try and find. First, get to Ultimecia’s Castle, and send the party of people you plan to use over to the Switch Parties Point nearest the Cathedral in the Castle. Then, switch to your unused characters, and have them run to the bell that, when you pull it, you hear “monsters roaring in the distance” or something like that, then switch back to your main party. Run to the Cathedral, and you see Omega. Run into him, and the battle commences.
Step 7: BATTLE!!! This is one of the fastest parts of this tactic. Battle opens, and Zell, with the Initiative ability, goes first, and uses Cerberus. Quistis follows by using Triple Aura, and Squall uses a Holy War. Now that Omega can’t hurt your three characters for a while, rain Holy Terror upon him. Have Zell use his Endless Rush Limit (keep cycling Beat Rush and Booya), Squall keeps up Renzo, and should end up using Lion Heart a lot, and #3 casts Triple Meltdown the first turn, then Summons and Boosts Eden to 250 for the rest of the battle (easily doing 25000 – 30000 each summon). Note that any elemental damage will heal him, but a Phoenix Pinion/Summon at a crucial moment is worth it. If you've used it before, then that's even better, as Phoenix may show up if, somehow, Omega manages to kill off your three heroes. Aura will wear off before the Holy War, so switch Zell to summoning Cactaur (hopefully lvl 100, to deal 10,000 damage), and Squall to Bahamut, who should do 9999. Keep up the pressure, and when Holy War wears off, have Quistis recast Triple Aura, then have Squall use another Holy War. If Zell or Squall can sneak in Haste, then all the better; you'll be able to do damage faster. Keep this up, and Omega will quickly fall before the might of your three chosen characters.