Take their newest album for instance, Pandora's Pińata. First track is heavily swing inspired and extremely catchy. The next is.. I don't know what to call it.. mexican? Then the third is more like metal (with cellos and trumpets), but with a very catchy calm and almost folk-like chorus as well. Later on, we find a full-scale opera track and a track that's more rock-orientated with a heavy funky bass. Not two songs sound alike.
Avant-garde is characterized by being very experimental and unorthodox. I say that fits Diablo Swing Orchestra very well.
As for Muse, I agree with you. However, I still think they have some vibes that are a bit prog-like. They also have very different songs with a lot of different styles.
I won't talk about The 2nd Law, though. Yuck.