To answer in reverse...
A external hard drive works exactly the same way as a memory stick, they are just larger in capacity (and physical size)
Yes it is possible to put you Itunes library onto an external drive, be it a memory stick (if big enough) or an external hard drive, obviously though the library would not be accessible unless the drive was plugged in
But.... you say your C drive is running out of space, is this the only hard drive you have listed in your computer. or do you have a D drive as well (that's not a CD drive) because if you do you can move some of your stuff there instead.