I have three computers, all connected to the same router, which goes to the same high-speed internet connection. Is there an easy way to transfer a few gigabytes of files from the two Windows XP machines to the one Linux machine through the ethernet cables?

yeah very easy , just setup samba in your linux box then u can simply copy and paste from yr win pc to linux pc

If it's just a one time thing & you don't want to bother with a samba setup, you can download "pscp" which is an scp program for windows. (google "ssh putty"). With that, just open a command line in windows and push/pull files just as you would with scp between linux boxes. If you're afraid of the command line, there are several GUI frontends to scp for Windows.... but I don't know any of their names.

Alternatively, it's pretty easy to setup a windows box as an ftp host, though I've had timeout issues with very large file transfers. 1 gig or so shouldn't be a problem assuming you've got fast interfaces/switches.