After a few tries I managed to get Portable OpenOffice to work on a USB memory stick. However, a new issue has come up:
I tried recording a very simple macro, for testing purposes. I selected some text and made it bold in Writer. After saving the macro in a new Library, I tried the command "Run macros...". As soon as I do that, the program immediately exits with no warning or any indication of a problem. I restart the program and it goes into crash recovery, but the macro is nowhere to be found.