When using iMovie it could be tricky as Apple has opened the many different file formats out there for iMovie so from Apple and a few other sites here is some info on the supported files I am giving you the following list as I do not what the .Mov file info your importing
The .Avi what is the format? and the export of the .Mov what was the settings that you used? If you want hit me with an email or you could read up on the file formats.
http://support.apple.com/kb/HT2264
http://support.apple.com/kb/TA22875?viewlocale=en_US
UPDATE:
David I came back and reread you post and the lake of audio is due to not having any of the following plug-ins and add ons to QuickTime so here is the list:
Perian (A Must have for any QuickTime Playback)
http://perian.org/
FlipForMAc:
http://www.microsoft.com/windows/windowsmedia/player/wmcomponents.mspx
Divx another must have:
http://www.divx.com/en/software/mac
3Vix:
http://www.3ivx.com/download/macos.html
Xvid:
http://n.ethz.ch/student/naegelic/download/
That'll do ya..........