I have both versions of Diablo 3 for the Xbox 360; the original game disc, and the Ultimate Evil game disc, would I be able to download all content from the Ultimate Evil edition onto my Xbox 360 and use the original Diablo 3 disc to play the expansion? My Reaper of Souls game disc is all scratched up and freezes on the opening loading screen.
If you own the individual DLC packs, separate from the Ultimate Edition, then yes. If not, you will have to purchase them separately.
Additionally, you can repair the disc (most video stores and game stores provide this service, for a fee).