My muses don't talk to me. My muses don't look like chibi angels. Plot bunnies, plot hermit crabs, plot Komodo dragons, and plot llamas do visit my head, but that's a topic for another meta. So my muses aren't "traditional" like perch_and_creep's but more free-floating like unanon's. But my muses are at the same time bound by very strict outlines.
My muses are like actors that never, ever drop their roles. They'll interact with each other, but only within the story so that they're "in character." It's like they're handed a piece of paper with a scenario on it and then they improv the scene over and over again, saying and doing different things until they hit upon the one everyone likes. I'm not even the director but just the observer . . . and the observed. It's a weird balance. As far as my muses are concerned, I don't exist. In all of my stories, I'm the outsider.
However, I can sort of fit into the story (not in the Mary-Sue sense, but in the sense that the story flows well, "fits" well so that the end product is something I'm proud to put my name on) by having one of the muses become me. Not vice versa. The distinction is important: I don't become the muse; the muse becomes me. I prefer saying it the other way around because it doesn't give the impression that I try to get into my muses' heads. It's the muses who get into my head. Often, several of them get into my head simultaneously while I'm writing a scene that involves them or, in other words, while they're improvising a scene.
I mentioned earlier that, as far as my muses are concerned, I don't exist. Likewise, as far as my muses are concerned, anything outside their universe doesn't exist either. This includes other stories that they themselves are in. Clarification: I'm currently writing three stories, "Changing Over," "The Fisher King," and "Proxemics," which have Pyro as a major character. This means that I have three Pyro-muses running around my head. ChangingOver!Pyro is completely unaware of FisherKing!Pyro and Proxemics!Pyro, and the other two Pyros are in the same situation, even though they're all based on the movie version of Pyro. Each Pyro is unique to his own story, yet each Pyro also is the complete and true Pyro so they can't be collapsed down into a single uber-Pyro. This can get complicated when I write drabbles, because then each drabble spawns an independent mini-muse of its own. So right now I must have twenty little Pyros improvising somewhere inside my subconscious.
So there you have my story-bound muses: fanatical and schizophrenic method actors who ignore me.