You can run MultiBit on a USB drive in a portable manner if you include a Java runtime (JRE). You can use the same executable jar on Windows, Mac and Linux.
There is some help on how to do it here : http://multibit.org/help_runFromUSBDrive.html
If you have a shell script / bat file that runs 'local-path-to-jre/java -jar multibit-exe.jar' it will run across Win/ Mac / Linux.
Strictly speaking it does keep a local copy of the blockchain but it is the bitcoinj block chain so is less than 20 megabytes.