Final Fantasy IV Side Quest » Getting Odin
First of all, you cannot get Odin until you finished the Cave of Summon Monsters side quest, and he only appears after the Baron raid. To get the Summon Odin, go to the center in Baron Castle. The guards here will say that they keep hearing voices from the basement below. Take the eastern staircase and follow the path. Go through the southern door, then under the northern gate outside. Head west down the staircase, then go all the way east until you see a red carpet. The King's ghost will call Cecil's name, and after the scene here you must fight Odin.
Odin is similar to Plague from the Lunar Subterrane. He will start out with an invisible timer, and when it reaches zero, our party's done for. So, attack him furiously and use powerful Lit3, Edge's Blitz and Rydia should summon Indra. He doesn't have too much HP, so just focus everything on him, including Rosa. Rydia might want to slip in Bahamut if she has him.
After the battle, Odin will join you as a summon.