virtualdub is a great free program that can help reencode to a variety of codecs (MPEG-2 in your case). IIRC, Quenc is one of the better free MPEG-2 encoders, although I think HC is also free and has almost caught up to, if not surpassed Quenc. CCE is still the king of MPEG-2 encoders, but the basic version is around $60 USD. You can try a trial version of it that outputs with a watermark to compare quality and see if the $60 is worth it to you.
The other step is to reencode the audio to either AC3, MP2, or PCM. PCM is almost unusable for full length discs because of its size requirements. MP2 is only recognized as part of the DVD standard for R2 discs, and most of the free AC3 encoders are a bit wonky, although they have gotten better since when they were first released.
This forum has a good DVD backup subforum that might be helpful (a manual backup of a DVD uses many of the same techniques you will need). Normally I would point you to doom9.org, but their forums are down for a while. You should give it a try anyway and see if their guide section is up.