I want to build the best exterior corners for a house in a high wind (wind not earthquake) area. I will not ever use a 2 stud corner with clips for multiple reasons. However I would like to use a California corner (2nd example) instead of a 3 or 4 stud (last example) exterior corner if the 2nd option will be as strong? The physics seems to rely on the the direction the wind comes from and which wall is bracing from that direction of wind. So I get that, but I want to know if the 3 stud corner would be as strong as the other option? There is less surface area to nail to. This would be 2x6 construction.
Wind damage to the house is not likely to result from bending of the wall studs, even at the corners. Wind-induced damage will occur at the joints between the studs and the soles or caps.
The exterior sheathing is what will provide stiffness and stability to the entire structure. Use the design that will allow the maximum area of attachment between the corners and the sheathing. The "four stud" corner provides the maximum nailing area on both outside surfaces.
The "California" corner requires that the sheathing on one of the walls be nailed to the 1.5" narrow edge of a stud. Many framers will not build two-stud or three-stud corners, not because they are more likely to bend, but because they provide insufficient nailing surface.
If you're overly concerned about lack of nailing surface at the corner on the "open" side of the California Corner, add an additional stud about 1-1/2" from the face of the interior stud. Leaves you enough room to spray foam insulation behind it, and provides an added bit of nailing surface less than 12" from the corner. That 12" gap isn't going to give up that much in the physics department.
If you are committed to interstitial (inside the walls) insulation, and are truly all that worried about heat loss in the corners, you should consider using the "Massachusetts corner" construction:
This takes some patience and extra labor to construct, but allows interstitial insulation to flow completely around the corner.
The interior angle should be constructed separately, with lots of nails and perhaps even small metal straps across the seam. The easiest way to make the corner straight is to temporarily clamp the 1"x4" boards to a straight stud before nailing them together. The important thing is to make it extremely stiff to support the interior drywall corner. It looks like quite a departure from standard practices but it is actually a lot stronger than the two-stud corner with those stupid drywall clips.
Now you can concentrate your attention on those awful cold strips caused by all the other studs between the outside corners.
Your structure's resistance to wind forces is going to come from your sheathing and from having a continuous load path to the foundation. Wind will cause uplift forces on the roof, shear forces between the base of the wall and the foundation, uplift on the windward wall due to rotational forces, and the more obvious shear forces making your walls want to "lean". The studs are not what's doing the work in that situation.
Nailing surface is gonna help with the last one to keep your sheathing in place but not with the others. I know it's a little outside the scope of your question but ....just throwing that out there.
"The best exterior corners for a house in high wind area": Get the Simpson catalog and invest in a continuous load path. Hurricane clips and appropriate hardware from the Simpson catalog are your best friend. There are corner straps that will cover the bases if you really want that nice light California corner, and will do a lot more than an extra stud will.
The claim here is that the two stud corner reduces drywall cracking at the corner. Sheathing and bracing would provide the needed shear strength.