The only avi files I have heard about that play on some DVD players are Divx avi files. I am not aware of any player that will play quicktime files as such.
Many DVD settop boxes will play VCD or SVCD disks (mpeg files burned in a unique format onto CD disks). QT cannot natively create or burn them but there are commercial programs like Toast Titanium that will do so. Check your DVD manual to see if it will play such files. You may be able to use this freeware to convert the avi files to a format such as DVStream that the CD burning sofware can use:
Mpeg StreamClip. Alternately you could use Quicktime Pro ($30 from Apple) to make DVStream files for the VCD burner from the avi files. Be aware that all this transcoding may reduce the videoquality to unwatchable levels.