my experience...
use max birates for video and audio settings (software may have to compress audio if not at highest settings)
If this doesn't work then...
If all out audio clips are out of sink then its computer hardware...not enough cache when saving. After sync save video only in one file and audio only in one file. Then recombine, should resync easier this time, then save as complete file. This reduces hardware burdon.
If audio doesn't sync easily when saved by itself as one mp3 file then its a codecs.
Common good codecs are avi, with mpeg4 not .264 and mp3 highest bitrates possible for both. Test for sync after save. If this works then reload mpeg4 and then convert to a different format.