Well, here's a convenient list of Linux multimedia projects
. Also, your question has been asked many times at this site; try searching for 'linux video editing' for more posts.
Your post suggests that you are interested in DVD encoding. acid_kewpie, a regular poster on this site, has a project called AcidRip, a GUI frontend to mencoder. Search this site for acid_kewpie's posts. There are also DVD::Rip and gtranscode, both GUI frontends to transcode. Both mencoder and transcode are excellent encoding tools, far superior to TMPGEnc.
For a simple editor like VirtualDub, look for avidemux. kino is a consumer-level editor that's handy with DV cameras. cinelerra is a higher end editor with more features, but is relatively more complex to use.