I used this style of fan to get the neighbors cigarette smell (that seeped in through the goddamn walls) out of my downstairs. I had a two story apt, with windows like this, where W=window room and R=room without a window;

W|W R|W

The best airflow was for the top floor where the windows were opposite and the natural breeze could do its own thing, but the single downstairs window was good enough to clear out the cigarette smell on its own so long as an upstairs window was at least open.

You say your windows are all on one badly ventilated side; have a push/pull setup with the airflow. Use one of your current fans to bridge the gap at the stairs and it'll work great.

I found i got the most airflow when pulling in downstairs and pushing out upstairs, regardless of temperature, but i live in a hot area. Definitely test yours to see what works best in your situation.

I never tried using fans away from the windows as mentioned before me, but that's definitely worth doing as soon as you can, just to see how much it inproves your situation.