Well, I heard Square Enix mention that Kingdom Hearts III would bring back "forgotten masters," which could be a hint of Oswald being brought back.
I've actually had a conversation with my brother about this. Since Oswald has been confirmed to be Mickey's older brother, that made us wonder something... How is Mickey the King of Disney Castle, since it's usually older siblings that would take the throne? This is when we came up with a storyline for Oswald. We said he was gone for a long time to become a Keyblade master, so long, in fact, that Mickey and their father (the former king) assumed he was dead and had Mickey made the crown prince. The old king soon falls ill and dies, leaving Mickey to take over the throne. Oswald actually completes his goal of becoming a Keyblade master, but shortly after loses his heart. Since his is so strong, it does leave behind a Nobody (we took influence from Epic Mickey). He does not scramble up his name because "What's the point, I've got nothing to hide," and resides in the Forgotten World. Remembering how he is called as a Keyblade wielder to try and destroy the darkness, he tries to do exactly that. He is not completely unsuccessful, being powerful enough to get rid of a large amount of heartless at a time, he knows he can't do it alone, but this drive is what keeps him going.
He at first tries to reach Mickey, whom he knows is also a Keyblade master, but he can't send him any messages (they don't go through.) When Oswald tries to find out why Mickey isn't coming, he then hears that his father has passed away, and that Mickey was crowned king in his place. This makes him very bitter and resentful of his brother.
I'd say he would be a great big part of the story, mostly as an emotional arc where someone is against Mickey but not evil. He'd probably tell Sora that they "Don't need 'His Highness. (Refusing to call him by name.)' You can do it on your own." He, at first, is very abrasive toward the company, and in fact refuses to help calling them a waste of his time, but eventually helps out. Even then when either Sora or Goofy tries to thank him he replies with "I didn't help you because I like you. I helped because it has to be done."
He eventually gets his heart back after a reconciliation with Mickey, who finally found out that Oswald was alive, putting aside differences because it isn't what their father would have wanted.
