All songs from iTunes should be usable in iMovie unless they are DRM protected. iTunes uses AAC and AIFF codecs, both of which work in iMovie.
What version of iMovie and operating system are you using? When you say your iTunes songs are incompatible, what exactly is happening? Do they import into iMovie but just won't play? Do they display waveforms? Is the sound distorted? Is it possible that you have the sound muted? Do the songs play outside of iMovie? Do songs from other sources play in iMovie?
-- Rich