I think that Diamond City is located on Earth while Mario's adventures take place on another planet with no official name. In WarioWare, the Earth is mentioned sometimes (e.g. by Orbulon) and Wario's house contains even a map of Earth in WarioWare: Touched!.
Wario did already find a warp to Bomberman's world (Wario Blast), so why shouldn't he find a warp to Earth, too? In the city Wario got a secondary residence, maybe it was sometimes boring in his castle because his only real friend at the castle seems to be (beneath himself) a hen (Wario Land II).
Also, Wario uses his purple car in Wario Land 4, and it is revealed that Dr. Crygor built it. That means that Wario already reached Diamond City some time before the events of WarioWare. Jimmy T. tells in the manual of the first WarioWare "...he (Wario) and I go way back", too.
I think that Wario changes between the worlds, especially to ensure that no one has stolen his treasures in his castle and to amuse with Mario and his friends. So far, that's my theory. And because of my bad English, German is my native language.