Hi,
Open your iTunes library from the iTunes app, and confirm that the songs are actually downloaded and not in the cloud. Download any songs that have a cloud symbol.
Check to make sure that the songs are not DRM (Digital Rights Management) protected. Any songs purchased from iTunes before year 2009 would carry DRM protection, that makes them unusable in iMovie.
The data profile on your post indicates that you are using early Mac models. You might need to do some software updates to make everything in sync.
You also can try deleting/resetting preferences. To delete/reset preferences open iMovie while holding down the Option and Command keys and select to delete preferences in the box that appears. iMovie will open in a new empty library. Reopen your old library to get back to your projects. Possibly you may need to reboot to set the changes. Deleting preferences is a safe procedure that will not cause data loss or disruption to your project.
-- Rich