Man,I'm in levels 50 (well, I was, my emulator got all saved games corrupted after I played a little bit of DBZLOG2) and couldn't beat Omega and didn't bother going to Shinryu, I believe that it was because that book that says: "First came the one without heart, Omega, then the one who followed him, Shinryu, whatever you do just let them rest since even the 12 warrioirs couldn't beat them" (it's not this exactly) and after this I started to believe they were almost impossible.

And almost the same storie happened in the Dawn of Souls, in the Soul of Chaos.

lol... i have the strategies for defeating them both like a bunch of whimps. but they are cheap oens.
for omega kii, use the song that sotps monsters. get like 3 bars singing it, and all with herma sandle. one guy needs to be able to heal, just in case. rest should have backup rapid fire in case omega breaks free and uses encircle.

neo shinryu: wow, my fav monster. i like the battle music.
anyways, have everyone with hermas sandles on, level 70's or higher. everyone jump (2 dragon lances on each guy) all will miss. do it again. tada. neo shin dies. but you must jump fast. dont wait 2 seconds then press jump. do it fast.

tada!
man, this is so easy ^^

I found Omega Mk II to be shockingly easy. He's really not any harder to defeat than the original Omega if you know the right strategy. And speaking of that strategy, here it is:

Make sure you have one character (I used two to be safe) equipped with two weapons that can be used with Spellblade (I used Ragnarok and Apocalypse on my main attacker, because they're the best you can get). Now, to defeat the original Omega, all I had to do was cast Spellblade Thundaga on my main character and then use Rapid Fire to take Omega down. It took me two turns, at the most. Omega Mk II is just as easy to take down; however, there is one thing that he throws at you to make the battle more difficult. Instead of being weak to Thunder-based spells like the original Omega was, Omega Mk II has a barrier that makes him vulnerable to only one type of spell at a time. You can use a summoner to determine what spell it is (don't use a black mage-Omega Mk II has auto-reflect). It'll change its barrier pretty quickly, so you may have to guess which Spellblade spell to cast. I used my summoner to summon Ifrit, and it damaged Omega Mk II, so I knew he was vulnerable to Fire spells. However, he immediately changed his barrier, and I had to guess which Spellblade spell to cast on my main character. I guessed Blizzaga, and I ended up being right. Just remember:

Dual wield (Apocalypse and Ragnarok)+Spellblade [whichever spell Omega Mk II is vulnerable to at the moment]+Rapid Fire=Omega Mk II pwnage.

Oh, and Coral Rings come in handy, too. If you have them equipped on your party, they won't take any damage when Omega Mk II attacks with Atomic Ray.

EDIT: I BEAT NEO SHINRYU!! And holy crap, he was hard. But surprisingly, it only took me about four attempts before I finally defeated him. Here's the strategy I used, although I can't guarantee it will work the first time you try it (there's quite a bit of luck involved in this battle):

CAST FLOAT ON YOUR PARTY BEFORE THE BATTLE!
I had one attacker equipped with two Dragon Lances who knew the ability Jump. It doesn't matter what other ability they have-they'll be jumping during the entire battle. My other three party members were support characters-I had two who knew White magic and one who knew Time (having the ability Dualcast or making your Time mage cast Quick helps a LOT). I had the two characters who knew White constantly healing the party, and I had the Time character cast Hastega and Float on anyone who had been KO'd and revived again. The first time I tried this strategy, the battle went up in flames right away. But the second time, luck must've been on my side, because the battle didn't seem all that hard. (My two characters who knew White magic would actually run out of things to do during the battle because my characters were almost always at full health.) That's basically how you win this one. Oh, and the reason why I think it's so important to cast Float on everyone is that Neo Shinryu will cast Earthquake when you defeat him (he'll also cast it at other points during the battle). He also casts Gigaflare near the end, but that really doesn't do a whole lot of damage to your party.

Having these items equipped helps a LOT:
-Force shield (if you equip this on one of your characters and cast Float on them, they're virtually invincible)
-Ice shield (this will absorb any ice-based attacks Neo Shinryu throws at you, and it really comes in handy)
-Coral ring (I had these equipped on all of my party members. It'll absorb Neo Shinryu's Tidal Wave and nullify the effect of any Fire attacks he uses on you. The only downside is that it makes your party more vulnerable to Lightning attacks.)
-OPTIONAL: Hermes shoes (I didn't use these, but you can substitute them for Hastega)

ha i found both omega and shinryu to be nothing but jokes i beat him at al lvl 40 and one lvl 39 the where pretty easy if you know what you are doing

meh omegawas a joke shinryu was a LITTLE i mean a LITTLE hard

They are strong but with the right stuff equiped and your strongest attacks they dont stand a chance.

did you guys ever try casting mighty guard (im guessing you found it?)
its a blue magic spell very hard to find though

I tried Omega MKII recently; he was hard yet I found the original Omega harder...

Shinryu was a joke but Neo Shinryu... we were the jokes.

I beat Omega Mk. II lke this

Bartz: Free Lancer,Spellblade,Rapidfire
Ragnarok,Apocalypse(inside sealed temple)

Lenna: Mime,Dualcast,time,white

Krile:Freelancer,blue,White

Faris:Mime,Dualcast,black,summon

I only showed Bartz's weapons becuase there the only ones important(tho you may want to equip some flame sheild) What I did was keep on making Bartz defend(because if you hit it with its weakens through an attack, it heals itself)and I put up the usuall stuff. Then I I casted ruby light and reflected its weakness 5 times and then made bartz rapid fire with its weakens.

For Neo Shinryu, I had the same set up but Lenna had the Force sheild(HELPS SOOO MUCH)and Bartz with two Dragoon lances and Time and I just kept on using quick and Jump until it dies. You may want to watch out because when it dies, It uses Giga Flare and Meteor.