Most of the songs are by Smash Mouth, and are already available on their previous albums. According to the internets, their cover of Under Pressure is not available in any format besides in the movie.
edit: Found some more specific info for you:
"Smash Mouth will be contributing the majority of the music for the film, including brand new songs So Insane and Everyday Superhero that can only be found on the band's upcoming release Summer Girl (in stores this summer 2006). Some previously released Smash Mouth tunes will be in the film as well, such as Hang On (from Get The Picture) and Come On Come On(from Astro Lounge). In addition, there will be a cover of the Queen/David Bowie classic Under Pressure and another SM original called Days Like These."
Songs by other artists: Superman by Five For Fighting & Hear You Me by Jimmy Eat World.