It seems as though .avi format is not supported by quicktime(the player on your Iphone). So, you could convert all of those videos to a format supported by your IOS device(mp4,mov,m4v) using VLC and Handbrake but this is very time consuming and less than ideal.
Or there is a program that can convert those files on the fly for you, but requires using your computer as a server to convert the files for you as you stream them to your device. A little setup work, free, and might be at least a temporary solution.
http://www.airplayit.com/blog/tutorials/watch-avi-video-on-iphone-ipad-without-conversion.htm
