Convert AVI to APK

Since you cannot directly convert images or videos to APK format, it is, per se, not possible to convert Audio Video Interleave Files to Android Package Files (.avi to .apk conversion). 

You could, however, use specialized apps, such as the Live Wallpaper Creator, which allow users to generate rich/animated wallpapers for Android devices from images and/or videos. Such wallpapers are typically created as APK files, i.e. programs, which can be installed and run on an Android device replacing your current wallpaper.