I think she gets some of her inspiration from Alfred Hitchcock (Bad Romance has mentions of some of his movies). And plus, the videos are just weird/spooky.
I disagree when people say she's over the top or she tries to hard. First off, how could anybody ever think of the stuff she does? I'd never think of cigarette sunglasses. Or a telephone in her hair (from the video Telephone).
I see as being all of her thoughts, completely unfiltered. Her music, lyrics, and videos are all thought out and planned, but there's definitely free-form. She doesn't dismiss any idea as crazy or weird.
That's part of her reason, too. She does this weird, crazy stuff to allow all her little "monsters" to open up.