Have you actually seen these "funky e-mails" that they've been receiving? (i.e. did they print them out for you to see?) Those e-mails might give you a clue as to what it is. If it's just gibberish, then it's a program messing with your computer likely. If it's "free sex here!" type things, then likely someONE is messing with your computer. Not entirely factual; but likely.
If you turn off that computer for a week but they still receive e-mails (within that week), then it's not your computer: it's someone else's (or your servers'). Try it and see.
