HELP! I have a fly problem (the bug, not the zipper)

OK, so I just moved into this new apartment, which is in a large converted barn. It is very cool and I love it, except for one thing: the flies. In the last week, I am not exaggerating when I say that about five hundred of them have died under my sky light and in my bathroom. They congregate around the upstairs windows, buzzing and swirling and driving me and my cats nuts. I have sprayed, so they do eventually die, leaving corpses all over the place, which is nasty as hell. Fly strips are completely covered in three days.

What can I do about this? I spoke to the landlord, who also lives in the barn, and he said he has them too, and it’s just the nature of the beast when you live in a barn. I cannot quite accept this. Is there any way I can keep these bastards out of my house? Killing them is not the hard part; I don’t want to deal with them at all. Anyone else ever live in a converted barn? Have you had these problems, and if so, how did you deal with it?

Thanks.

Screens, oodles and oodles of screens.

A huge pile of manure, somewhere away from your barn.
Negatively pressurise your barn.
I’d also go with screens.