If you're trying to watch a downloaded movie onto a DVD, you have to burn it as a DVD video. It's not as simple as just putting the .avi file, etc onto the disc.
You need to lookup how to burn a movie file to a DVD playable in a DVD player, then use the Xbox as a DVD player. Mind you, the Xbox does need the DVD remote kit in order to play a DVD. The kit comes with an IR receiver that goes into one of the controller ports and you use the remote to control it.
edit: I just realized you're using an Xbox 360, which has a lot more versatility. But what I do recommend is, you setup a home network and share the media files, then you will be able to play them directly across your network so you don't have to burn them to a DVD.