Kawamatsu no recognising minks confirms that he isn't one. Now... what is he though? Maybe Zoro was right and he really is a fishman.
Also, in case y'all haven't noticed, Oden is a big reference to Heracles from Greek mythology. Time to drop my evidence!
Looking at his labours, I think we can make more connections. He had to capture the Boar of Erymathia, paralleling Oden killing the Mountain God. He had to clean the Stables of Augea, stables notoriously filthy and filled with cattle shit, so Heracles rerouted a river and cleaned the entire stable in one day. Oden deadass lifted a river to clean the capital (though he fucking flooded it LMFAOOOOOOOOOOOO). Oden was disowned by his dad, Heracles was disowned by his "mom" (Hera). Also, Oden joined Roger's ship in their own adventures. In the same way, Heracles joined the Argonauts, a crew comprised of a lot of Greek mythological legends, in their journey to obtain the golden fleece, a story that in and of itself can be assumed to parallel the journey to find the One Piece.
But perhaps, most famous of all, Heracles' most well-known labour is slaying the Hydra. A myth that's similiar to the slaying of Orochi using two swords, one of which was received by a certain Japanese legend who Zoro takes a LOT after, and what a coincidence, Zoro now has Enma. Anyway, the slaying of the hydra... reminds ya of Orochi's devil fruit, huh? Considering how famous that myth is, it's possible Orochi and Oden's rivalry is much more serious than we think, though now he's nothing but some dumbass kid.
Now, to just dump my own random theory:
What if Oden got a devil fruit, the Orochi fruit? And we are told Oden was MADE into Oden, he was boiled alive, LITERALLY. What if... Orochi ate him? He always talks about "beating" Oden. And Yasuie before dying told him "someone like you will never truly DEVOUR Oden". If Orochi pulled a Big Mom to get Oden's devil fruit that's the most fucked up thing ever. Anyway post OVER