Alot of time the audio slip you are describing has to do with the fact that DVD is mastered at 48 khz and that Xvid video you have is probablly a 44.1 Mp3
The sync has to do with the audio sampling rate. Most Xvid movie players will auto correct for the sampling rate mismatch, however DVD players do not
Your best bet is to find a cleaner source of the file you are trying to convert, since converting Xvid .avi files are difficult enough to handle as it is.
However if you have your heart set on converting that one file instead of finding a better source, Assuming you have windows XP, installing the right codecs on your PC and using an NLE that operates off of Direct Show filters (Like Premiere, or Vegas) could allow you to drop the file into the timeline, and then you could export to DVD from there.
Try Downloading ffdshow, or Defiler codec pack, and run the files through your NLE. You may be able to render it
If all else fails, Use the TV out function on your video card, get a mini-->RCA jack converter and run the video into your DV cam and hit record. Record the whole material and drop it back onto your PC, do the normal DV-->DVD conversion from there.