Can you play terraria of off a usb

Yes you can, just make sure you install the game to it. Although it's a small game I'd recommend any storage device of at least 2GB. You might also experience some slow down in the game because flash drives aren't as fast as your computer or console's hard drive.
EDIT: Add these dll's to terraria folder so you don't have to install xna framework, making terraria %99.9 Portable ( Portable means works without installing anything ).

Copy this in your address bar to go to mediafire to download dll's :) --> bit.ly/1QcJQA1