iv read about it. how it works is that when you soummon odin onto a monster that is death proof then insteed of failing it willl do damage. how much damage is a mystery to me but it takes a lot of ability crystals to equip it so its recomended that you only equip it if your going to use odin alot.
Look it up somewhere, must be useful for something
Anyhow, first of all you need Odin, which garnet can learn from the item "Dark Matter." You can get that from the auction house in Treno. Then, go to Ipsen Castle, in the north of the forgotten continent. Now my memory is a bit shady on this, but I think that if you take one of the pathways in the first room you enter you come to an open space with four pathways, which are converging in an "X" to a pillar in the middle, which is an elevator. (If you can’t find the room, keep looking, because I am positive it is in Ipsen Castle.) Take the elevator down and you will come to a room with a giant, glowing sword, which is crackling with energy. You will have to do a simple puzzle by moving a pot or something around, I can’t remember how it worked, but it was really easy so I won’t bother explaining it. Anyhow, when you do that, you get the item "Ancient Aroma" (or something like that), and it gives garnet the ability "Zantetsu Damage." Since I wrote that post I’ve trained the ability and cleared the game, so I’ll answer my own question. Yes, Odin does damage when summoned, and though it’s not particularly high (I think Bahamut and Ark deal a tad more) it is worth getting, because the MP cost of summoning Odin is much cheaper than Bahamut or Ark, and because it doesn’t take much effort to get.
I think his attack is wind-elemental, but I may be wrong. And I think you can increase his attack power by getting more Lapis Luzilz (sp?) into your inventory, but I may be wrong about that too. It’s been awhile since I remembered info. on Odin.
In the last battle, my Garnet did it and constantly Ark appeared eveytime 5 or 6 turns passed.
That helped me a lot.