There's also songs that may have been initially inspired by a certain other artist but strayed far enough to be basically completely original, such as Albuquerque and (possibly my favorite Weird Al song of them all) Hardware Store.
Not to mention the polkas, which is what I really had in mind when I was talking about him making other genres rock.
Also, The Presidents of the United States of America.
The song "More Bad Times" came on my Spotify radio playlist a few years back. I had never heard the song before. I was dying of laughter. I was not at all prepared for a song that silly.