How to get the Odin Summon in FF4
Note: In order for you to obtain the Odin Summon you first need to obtain the Asura and Leviathan Summons from the Land of Summons. Until you complete both of those side quests, this one will be unavailable.
To obtain the Odin Summon you'll want to first visit the town of Baron. It's highly recommended that you save your game before entering Castle Baron as the upcoming boss fight will be challenging. Our destination is the basement of the eastern tower in Castle Baron.
Much like the Demon Wall boss fight, the fight with Odin is a race against time. Odin has a total of 20,001 HP and if you're high enough level (in your late 40s) the fight will be a total piece of cake with Rydia. Odin is weak to Thunder magic and if you have Thundaga it hits for 9999 damage in total. That means it's basically two rounds of Rydia using her most powerful magic to take out Odin.
If Rydia is too low level and you find this fight to be too difficult you can always wait until after you go to the moon and FuSoYa joins your party. At that point in time the fight will be much easier with the additional party member. Much like with all the Final Fantasy games, if you take too long to defeat Odin he uses his signature move, Zantetsuken which deals about 5 - 6000 damage to your entire party.