Aipom will evolve in the 3rd Gym Battle.
Staravia will evolve after the fifth Gym battle, but before Iron Island.
Turtwig will evolve before the 5th gym Battle, but most likely after the 4th.
Ash will get a Riolu egg in Iron island which will quickly hatch into a powerful Riolu that Ash will train for a few episodes on Iron Isle. By the 7th gym, it will be ready to fight in a gym battle.
Grotle will evolve during the Sinnoh League sometime.
Ash will also get a Glaceon around the time of the 7th gym.
Correct me if I'm wrong here, but if this were to happen wouldn't this be the first time one Ash's pokes evolved during a gym battle? I can recall quite a few times when the opposing gym leaders pokemon evolved (Sabrina's Abra to Kadabra, Brawly's Makuhita to Hariyama, etc) but I'm pretty sure he's never had one of his team evolve in an official gym battle. Either way, it would be cool to see this during the D/P saga, regardless of which of his pokemon it occurs to.Aipom will evolve in the 3rd Gym Battle.