FFMPEG. The only converter you'll ever need for anything and everything. 30MB, no installation necessary, put it wherever you want. It has no GUI, but it's very easy to use in command line.
ffmpeg.exe -i " video.mp4" "audio.mp3"
Of course, there are a plethora of other options for controlling quality, and tons of other supported formats.
If you're really not comfortable with command line, there are GUIs like WinFF or MyFFMPEG you can get for it, but then you lose a bit of the minimalism you seem to be going for.
Depends on what 'functions' you want. You just want to split video files? There is the ones i have used for ages.
winff - http://www.biggmatt.com/winff/
avidemux - http://avidemux.sourceforge.net/
There is also 'Kino' but i think it is no longer being developed.
Actually, as a final step, I used WinFF to convert my MOV into a webm. You should be able to do the same with an AVI, if the only thing you're looking for is a smaller size.
The exact version of WinFF I use might not be available? Guy seems to have gotten rid of the old site so I'm not sure whether the latest version of WinFF supports WebM or not. IIRC I had to go through some hoops on his old site to get a 64-bit version just for WebM support.