You can run MultiBit on a USB drive in a portable manner if you include Java runtimes (JREs) for the operating systems you are interested in. By including a JRE on the USB drive you can be sure it will run on the target computer. MultiBit runs on Windows, Mac and Linux.
There is some help on how to do it here : http://multibit.org/help_runFromUSBDrive.html
You can create a shell script / bat file with the single line: 'local-path-to-jre/java -jar multibit-exe.jar' to start it up using your included JRE. (Note that Macs are guaranteed to have Java installed so you do not need a JRE for that platform.)
There is a detailed tutorial on how to install the java JRE here: http://www.dreamincode.net/forums/topic/42544-putting-java-on-your-flash-drive/
You can store your MultiBit wallets on your USB drive. By default the path to the wallets is stored in the MultiBit config file multibit.properties as an absolute path (i.e. with a drive letter/ name). I think you can tweak this to put in a relative path which would then open automatically on any computer. Alternatively you can just go to the 'Your Wallets' screen and press the 'Open Wallet' button to open it manually.
Strictly speaking MultiBit does keep a local copy of the blockchain but it is the bitcoinj block chain so is less than 20 megabytes.