You don’t say much about your avi file.If is a Xvid file VSO DivX to DVD is a freeware and you may try it.Also I found another converter reading Video Help site about Main Concept H.264 and I try it, is fast like
WinAvi or VSO but the trial is going to put a logo on your video but is working.Google VSO or MainConcept and play with but synch problems are very easy to find it with VirtualDubMod.The frame is different between the video and audio.Most of them come from codecs collection so you want install a Ace Mega Pack from here:http://www.free-codecs.com/
Before you start converting check the file with GSpot or Avicodec and be sure you have all the codecs and only after this start the convertion.Here is a link to a codec wizard does not hurt to try it:http://www.
afreecodec.com/codecwizard/