When banished, normal daedra end up in the Waters of Oblivion and have to find their way back to a Plane of some sort, but what happens when a Daedric Prince is banished? Does their Plane end up displaced or temporarily cease to exist or something? Would all the denizens of their realm end up lost in the Waters of Oblivion as well?

They go back to the waters as well. Their realm still exists, but they simply aren't there and good chances other Princes might come along and mess it up. The big unknown is what happens to a Prince when they return to the waters when they have no realm, like Jyggalag.