How do I rip a dvd including menus and extras to a menu driven divx file (or any lossy format that supports menus)?

Try Dvdrip.

Dvdrip is a full-featured DVD copy program written in Perl. It provides an easy to use, but feature-rich Gtk+ GUI to control almost all aspects of the ripping and transcoding process. It uses the widely known video processing swissknife transcode and many other Open Source tools. dvd::rip itself is licensed under GPL / Perl Artistic License.¹

To Install Dvdrip, do that from the USC

^{1Source: Ubuntu Documentations}

Another program is HandBrake. I don't think it can do menus, but take a look at it, you might use it for other projects.

I just stumbled upon AcidRip DVD Ripper. You can install it from USC. From reading about it, I think it can do menus, but I'm not sure. I* will test it once I'm done with the project I'm working on.

Take a look at this:

k9copy provides the following features:

• The video stream can be compressed to make the video fit on any configurable target size
• DVD Burning
• Transcode DVD using mencoder or ffmpeg with configurable presets
• Creation of ISO images
• The possibility of choosing which audio and subtitle tracks to copy
• Title preview (video only)
• The ability to preserve the original menus ¹

^{1Source:Ubuntu Apps Directory}