I don't know multibit, haven't tried either on Debian or in Whonix, but I see two possible causes for errors here.
How did you install openjdk? From Debian package sources? If not, uninstall what you installed. Then install from package sources.
sudo apt-get update
sudo apt-get install openjdk-7-jre
That might work better.
Also "No protocol specified" might imply you tried to start a graphical user interface application as root, which is recommended against. Start is as user, without using sudo.
multibit instructions for Debian stable (currently: wheezy) should also work for Whonix (which is based on that Debian version).