The MP4Modifier isn't a good answer. AVI isn't suppose to carry AR information so many players (MPC, standalone, etc.) tend to ignore whatever you patch it as.
MKV natively supports pixel and display aspect ratios and makes a good alternative, but it will of course be unplayable on standalone units.
Btw, conventional wisdom would have had you also crop the black bars on the top and bottom to save bitrate. (Would have also preferred the original DD5.1 track to mp3.)
...but no one EVER gets their first DivX/XviD encode attempts right. :-)
Really try AutoMKV, it supports XviD as well as X264 and is a tweaker's dream.
Edit: The real problem is you exported to a lossless codec, which unlike an authored DVD contains no information about the display aspect ratio. You have to specifically set the resize and cropping.
In avisynth it would be: crop(2,58,-2,-64).Spline36Resize(844,356).
(Note: This overcrops by one line on the bottom, and slightly shrinks the video (about 2 lines vertically). The reason is that black borders are a sharp edge that Xvid codecs must spend lots of bitrate keeping intact. The resize brings the resolution to mod4 which improves the codec efficiency as well (without introducing aspect ratio error).)
A good way to go would be to create an avisynth script with those settings, use AutoMKV and select the AVS for the video, and the original file (or the .ac3 file if you have it, or mp3 if you want to use one you've already encoded) for the audio track.