Is it a Spanish clay-tile roof setup? Birds love those. If so, they do make clay caps that are SUPPOSED to be put in the ends of the open "tubes" created - you'd be stunned at how often they're omitted, left out or "VE'd" out by cheap owners (which of course ends up costing them a fortune later when birds get in there).
Get a cat.
You can borrow one of mine for a week if you want. It'd probably take Linus (the big one) about 15 minutes to take care of the problem. He's quite the hunter.