In a more comical take, Ron Weasley could end up in the DxD world and mistake a Devil for a new kind of magical creature. He tries to befriend it using his typical Ron - clumsy but endearing - ways. Meanwhile, Hermione is trying to figure out the scientific and magical laws that govern the DxD world. They all get involved in a school - tournament in the DxD world that combines magic and combat skills, much like the Triwizard Tournament in Harry Potter.
One idea could be that Harry Potter, while exploring some new magic, accidentally opens a portal to the DxD world. He then has to adapt to the new rules and powers there. Maybe he teams up with Issei and they use a combination of Hogwarts magic and Sacred Gears to fight off a common enemy.
Perhaps Voldemort somehow makes his way into the DxD universe and starts causing chaos. The Devil Kings in the DxD world are initially confused by his dark magic but then they join forces with Harry and his friends. Harry could teach them some unique spells from Hogwarts, like the Patronus charm, which could be useful against Voldemort's Dementors - like minions he might create in the DxD world.