Youtube videos?
Are those videos that you uploaded to YouTube, and now won't stream properly.
Or videos that you downloaded from YouTube, and the files that you downloaded now show that out-of-sync ...
Do you get ANY improvement after you restart your Mac, then immediately try your video?
If you stream those videos (try the worst one first) direct from Youtube, do you still have the sync issues, even from that original video?
As there are many sites that report problems with video/audio going out of sync, both Windows and other operating systems, you may have an issue that does not have an easy answer.
I would suggest that you can try dragging your user (home)/Library/Caches folder to the trash, then restart your Mac. There may be some odd cache file connected with video play that is corrupted in some way. Removing the entire Caches folder, then restarting (the folder will rebuild as needed) just might take care of your issue, if it is a user issue.
You can also try your video after logging in to another user account. If you get normal video play, then it may be something else in your normal user folder.