If your avi’s play well using VLC Media Player it might be worth converting them to MP4 using the ‘convert/save’ option in VLC’s file menu. VLC streams the media and records that stream, it’s not a straightforward conversion which is why I say if it plays well it will probably look good once converted.
If you haven’t tried using VLC for this purpose before there’s some quite good tutorials on the web which might help though it’s quite easy. Failing that I tried ‘handbrake’ myself the other day and was pleased with the results.
Best of luck! 
