I love Moulin Rouge for the music, the characters, the story, and the filmmaking style. I can't resist the sight gags, graphics, the performances, it's all so great, IMHO.
But, it's a flick that you either love or hate.
As for trying to "get" it... please don't. Baz Luhrmann called the style "Comedy Of The Heart". It's absurd, pointless comedy based on sight gags and simple things like the sound effects and cinematography. In Moulin Rouge, the movie itself is a character. Don't try to get it, just sit back, relax, laugh, and enjoy.