mpeg2 (and mp3)can be literally sliced up because of how they are structured so yes without remuxing.
Remuxing sync errors tend to happen when variable bitrate sound is used... a PITA that saves but a few MB.
Handbrake... newer versions are mp4 only but the one that does avi/xvid/mp3 is around still here (0.9.2). I have a simple gui as the linux one offered is a bit barmy.
Favourite convertor I use is Mencoder ... its fast and seems to make smaller files.... I am tending to use x264 now as it can encode using multi cores and makes smaller videos that are very impressive in quality. Again I have a simple gui for it to avoid the command line.
I assume ffmpeg can do it too... well everything linux uses ffmpeg in some form or other....its how the dvd is handled that varies.
Avidemux can be used !!!... you select the largest vob.... usually ok but sometimes you have extra parts to the dvd which may not be included or tagged onto the end. The other 2 can select titles and chapters and list contents.