Regarding the cross wind. We were getting severe cross wind gusts in flight so the tail was swishing for sure. Every time we would get a big gust the wind came through the passenger door and applied pressure to the pilot door and pop wide open. Also the cross wind gusts were going right into the oil cooler outlet preventing the outward flow of air and the oil temp spiked. I had to crab out of the direction fo the gusts. It was a particularly lousy day.
Like Ascend Charlie, I'm feeling a little puzzled about the whole gusty crosswind thing. If you were in cruise flight (even slow, like 60 MPH) a gusty crosswind isn't going to prevent the oil cooler from doing it's job. If the temperature was spiking, I think it's likely something else was going on. If you think about why the tail is twitching, it's because the natural weathercock stability the tail is providing (admittedly much less in an Enstrom than in other types) is trying to keep you in trim. When the wind gusts from the right, the tail is forcing the nose to the right to keep you in trim. When the gust subsides, the nose is being forced back in order to keep the aircraft in trim. In all of those cases, the airflow is still mostly from nose to tail and the oil cooler should be quite happy.
The door may be a different thing, but I suspect there's something else going on with the oil temperature. Especially given all the other things you've discovered rigged wrong with this aircraft...
I've been out in 45 knot gusts and never had an issue like you are describing... All my (Enstrom teaching) experience was in an F28A if it matters...