You don't have to listen to this show, I promise! Noah actually says not to listen to it, and tried his best to prevent this show from happening.
1. "Jingle Bells," Track 9 on the Tenchi Muyo! Ryo Oh Ki Christmas Album. Not available in North America (imports only).
2. "Joy to the World" although I don't know the Japanese name or track number, it's on the Tomoeda Shougakkou Chorus Club, a Card Captor Sakura Christmas album, not really available in North America. Try looking for it here.
3. I don't know what this track is called or which album it's from, but maybe you can figure it out by read this page. It's definitely from a Live Action Sailor Moon soundtrack.
4. "Christmas in the Silent Forest" by by Ilaria Graziano, track 10 on the Ghost in the Shell Stand Alone Complex OST 3. Apparently it was the fourth opening theme of SAC in the first season, but Cartoon Network doesn't want you to know that!
5. A Podsafe Christmas Song by Jonathan Coulton. You can download it from that link and use it on your own show and stuff. You can even give him a tip!
6. "We Wish You a Merry Christmas" also from Tomoeda Shougakkou Chorus Club, the CCS Christmas album.