Mkv is a type of container for various video and audio codecs. You can use mpeg, h264, VC-1, xvid, and many other forms of video within the mkv file, and of course there are many types of audio that will work within it as well.
So, when you talk about mkv files, you need to know exactly what is within them, just as avi files can have many different codecs.
The most commonly used codecs in mkv files are H264 video, and either AAC or AC3 audio. Mkv files can also have subtitle streams. You can find out exactly what is within the mkv file by using MediaInfo; just be careful not to install any “extras” when installing MediaInfo, because it does come with some crapware browser bar that you have to avoid putting into your system. The Tree and Text views within MediaInfo are the most informative.
It is possible to convert mkv to other formats, but if they are already out of sync in the original mkv file, conversion to dvd or avi won’t fix this on its own.
It is possible to demux (separate the audio and video streams), then remux them back into an mkv file and adjust the audio/video synchronization. This isn’t particularly simple, and you would need to know the amount of adjustment necessary. You could probably do this with an older version of AviDemux (version 2.5), and it can be done using mkvtoolnix and mkvcleaver or mkvextractgui2, though this second way of doing it doesn’t give you a clear understanding of how much adjustment is necessary.