I've climbed Mt. Langley quite a few times (~9) and summitted around 7. I prefer to bypass both Army Pass and NAP, and climb the SE ridge. It's listed as a Class 3, but only has a couple short sections near the top that are real Class 3. From Cottonwood Lake #5, proceed North to the uppermost lake, right below the huge cliff face. From there proceed up the gulley closest the face heading in a NE direction. There is a nice notch at the top of this ~1000ft climb. From there, proceed around to the left (NNW)for about 200 yds, to cross the ridge and into a drainage (very upper Tuttle creek drainage, I think). This will give you a view of the SE ridge of Mt. Langley. Slog up this drainage to gain the SE ridge and climb your way to the top, veering towards the Left or center of the SE ridge. Going too far over to the right (North) puts you into some pretty good exposure down the North face.
I prefer this route because you avoid most of the sand/talus slog up the South face that both the passes give you. Once on the summit from the SE ridge, I descend via Army Pass. I also prefer to camp at Cottonwood lake #3, and have taken water directly from the waterfall between lake #4 and #3 witout filtering and have never had ANY problems. The fishing has certain restrictions, along the lines of catch/release and using barbless hooks. I think Lake #5 is the only one that you can catch/eat. There are the biggest Golden Trout I've seen, though, in lake #5...upwards of 12-14 inches.
The shack you mention is a Ca. Dept of Fish/Game field shack. I think they use it during the summer when they are stocking the lakes, or doing studies.
There is no restirctions on camp sites, other than the usual distance requirements from trails and water. There are some nice spots on the NE corner of Lake #3. It's warmer there, and less windy, with a few trees around. Up at Lake #4 and #5, it's much more exposed. Have fun.
