Not all avi files are alike in configuration. AVI is a container format, and the codecs used within them vary quite a lot. Look at the manual for your player and see if it has specifications that are needed in the avi file in order to play them.
The most compatible and most common codecs for playing back avi files in a dvd player are xvid and divx for the video. Audio can be mp3, ac3 or more rarely, pcm. Examine the avi files you have that play correctly with a program called MediaInfo. It is free to use.
MediaInfo will tell you the codecs used in the files, the resolution, the frame rate and the type of audio.