The .DMG files are disk image files. You can mount these like you would an iso image file under linux as a loop-back device. Not something I've played with but from searching is would seem to be as easy as this:
You would need to do this as root so it would be:
sudo mount -t hfs -o loop myImage.dmg /macdisk
So you should be able t read the contents, but as iJack says no Mac application will run under Ubuntu.