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 have a copy of the blockchain but it is the bitcoinj block chain so is less than 20 megabytes.