If the video and sound are in sync in the avi, and it is off in the dvd-video prior to burning, you know the conversion process is to blame for the loss of sync.
One tool that can fix small problems in dvd-video sync is the Quickstream Fix tool in VideoReDo. VideoReDo TV Suite should be able to import the dvd files directly. This isn’t a free tool but the free trial is fully functional.
VideoRedo is an editor for mpeg2 files found in dvds, and there is a separate Audio synchronization tool for more stubborn problems.
Is the problem progressive or stay the same throughout? The progressively worsening synch problems are harder to deal with.
And you can always use a different tool for conversion instead of Nero. There are several free ones that can work for this including FAVC, AVStoDVD and DVDFlick.