Were these iTunes songs purchased recently, i.e, after year 2009? If so, they should not have DRM protection. Since the songs that you bought have DRM protection, something is amiss there. Possibly the songs are not showing for some other reason.
To cover the bases, open your iTunes library on the iTunes website. Pick a couple of the songs that you believe are DRM protected and not showing in iMovie. Control-click on the song's title. In the pop up menu, click on Song Info. In the pop up info box that appears, click on File at the top right of the box. At the top of the box,under the heading "Kind", it will show whether the song is protected and will also show the purchase date. The song in the example below was purchased in 2006, before 2009, and thus carries DRM protection, and is shown as a Protected AAC Audio File.

So, is the above what is showing for your songs ? If so, is the purchase date prior to year 2009? Did you purchase the song directly from iTunes?
If you don't mind spending $1.30 to repurchase a song that is shown as protected, try repurchasing and see if that cleanses it of the DRM protection. It should.
-- Rich