Have you already tried to replace any instance of F:\PellesC\ with nothing?
This way F:\PellesC\include will get include and should work on any computer despite from the drive the USB stick is assigned to.
There is no problem with relative pathes for include and lib directory.
The problem are the pathes of the addins. It seems that POIDE scans at the start for existing addins in the Addins-directory and if the are new they are added with the absolute path and switched off. Addins with are never existing at the absolute path are deleted. If you put your USB-stick in a computer where you get another drive id all addins are deactivated.
But I think, I will write a launcher application with changes the pathes in the XML-file of the addins and start POIDE. I need only a little bit time.