Does iTunes Match just 'match' your library with songs in the iTunes Store?
Apple scans your library, if it identifies your file as part of the iTunes Store collection, it will 'match' it. If not, it uploads the file to your cloud. In your iTunes library you should see an iCloud icon next to your filenames - use the Show View options to add the column 'iCloud Status' - that will tell you if the song has been matched, uploaded, or waiting. Check if your CD uploads are in the correct format to sync. 

If you right click on the song there's an option to 'Remove download' - this will delete your file off your local device. If you make a backup of your  current library, you could 'remove download' for your entire iTunes Match library - all the music should be stored in iCloud, and if it's matched, it will play the iTunes Store quality version. Sometimes there's issues with multiple devices on the same iTunes account conflicting sync.