This episode is part of the (entirely hypothetical) "Road To The _____" series of episodes. In these, Stewie and Brian go on wacky adventures. These always include at least one musical number. "Road to the Multiverse" is no different in that respect.
This episode explores the idea of parallel universes. Territory which, I quietly have to mumble, has already been thoroughly mapped by The Simpsons. In at least two Treehouse of Horror episodes that come to mind. Oh, and an episode of Futurama. And I think American Dad had one, too.