This post gives instructions on how to make multibit HD portable. I have never used multibit HD myself and I can't vouch for the instructions. Could anyone who tries it out post here and let everyone know if it works or not?
RE: portable mode. We don't advertise the feature but yes you can run it in portable mode the same as MultiBit Classic. Put everything that is stored in the user directory in the installation dir and it will pick it up
We don't advertise this feature as we know that inevitably people will lose their USB drives (and have no backup set). Then they will email us to ask us to recover their bitcoins. If they don't have their wallet words they just lost their bitcoins and we cannot do anything to help them. We don't want this to happen hence don't really advertise this feature.