It entirely depends on the audio track.
VirtualDub (
http://www.virtualdub.org/) can help you extract the audio out as a WAV, but then you have to work out what you're going to do.
First of all, if the audio track is mono, forget it - this is impossible.
If the audio is in stereo, you can get rid of most of the vocals (provided they're strictly center) by subtracting one channel from the other. This has the effect of cancelling out all audio that is exactly the same on both tracks (ie, only the vocal track if you're lucky) whilst retaining the music. (Note that the music will become mono.
http://audacity.sourceforge.net/help/faq?s=editing&i=remove-vocals)
Adobe Audition has a Centre Channel Extractor which can do the same thing (using a different technique which will enable the music to remain stereo) but your mileage may vary.
Also, note that the more compressed your audio file is, the crapper this is going to sound. If the audio in the AVI is 128kbps, you're going to hear a lot of bubbling remnants of speech, and whatever the bitrate you'll always hear some.
If the vocals have reverberation or echo on them, the echo will remain.
SFX you're basically stuck with unless they occur in the centre channel also.
If the audio track is 5.1 Dolby Digital, your life becomes a little bit easier, because you can just kill off the center channel completely. BeSweet will enable to you export each of the six tracks as an individual MONO WAV file. Import them into a multi-track editor (Audacity again...) and throw away the centre channel. Sometimes you'll find that the effects are stronger in the back channels than they are in the front channels. If you're clever you can chase the effects around and get rid of most of them. (For instance, if you have a sound effect that starts off front left and moves to the back right, you can crossfade between the front RIGHT and back LEFT channels, avoiding the SFX and keeping the music intact. This can sound really pants because you're panning around the music as well, but it's better than nothing if you're really desperate.)