No, OneNote cannot be installed to a USB memory stick. The closest you could
come would be using Virtual PC to create an virtual Windows install, install
office in the virtual machine, and then save that image to the USB device.
On the other hand, if you want to take data from OneNote and carry that
around, you can export to PDF or HTML and save those docs on the memory stick.
Last thing: if your friend has OneNote, you can create a notebook on the
memory stick and carry it around with you. It will work on any machine with
OneNote installed. I do this myself with three notebooks and they all work
fine. Just make sure you both have the same versions of OneNote.