Try listening around the window to see where the noise is loudest. It can help to use a piece of mid-size tubing (maybe 3/8 to 3/4 inch diameter) as a stethoscope of sorts. Hold one end firmly to the ear and probe around the window with the other end. Sounds will be carried through the tubing and you'll be able to localize them better. Listen around the woodwork/casing around the window too, not just points on the window unit itself.
I'll guess that there's not a lot you can do about sound which transmits through the glass. The seal between the movable pane and the fixed pane is a likely place for sound to enter, and this one you may be able to easily improve. If the window is opened never, seldom, or even just seasonally, then foam (weatherstrip) pressed into the gap or tape applied over the gap could help. Watch out not to damage the brush/seal that's already in that space.
You might also be able to determine whether noise is created right there at the window. That removal of the screen helps suggests this could be the case. Experiment in that area a little more. For example, try fitting open cell foam in the space between the screen and the glass on windy nights. Something like a camping mat -- thin foam might be found at a craft store. It'll prevent the screen from vibrating, and it may reduce the noise of wind swirling around the edges in that space. Another experiment to try is externally applied shrink film (find it with other weatherization products in a home center). That may help the air currents to pass by the window with less turbulence. The film would need some support in the middle (the foam would do) to prevent it flapping and vibrating, especially if the window is large.
Also look/listen in other places -- sometimes wind noise comes through wall penetrations for electrical and low-voltage outlets or other unexpected places.