I have cut up a couple into boards. They do have a smell when green/wet but when they dry out the smell is gone. Cottonwood cannot be used where it will get wet as it will deteriorate real fast. There is a pallet mill about two hours from you in Hatton, ND that uses only cottonwood.
One problem with it is that you have to cut it up as soon as you down it because it will start rotting in only a couple days. That's why the pallet mill will only use what they cut down, (I asked them).
It can be used for inside furniture, like work benches. My work bench is made from one that I cut up. It looks like pine but is a little heavier and holds up to being banged around and heavy equipment on it better than pine.
I have a loose piece in my garage that is just air dried and planed, I give it to people and they cannot tell me what kind of wood it is. It doesn't have that bad smell when it's dry and that confuses people.
To sell, forget it, you might be able to give it away if you find some one who is not ignorant of its qualities, like what was said above, you can use it in horse stalls because the horses won't chew on it. But like you said, here in ND it's everywhere. I haul most all of what I cut down to the dump.