What are these horizontal & diagonal 'studs' in the wall called?
This is bracing that is needed for a shear wall. This provides lateral support, which is needed in areas prone to hurricanes and earthquakes. Typically, the plywood sheathing and drywall is all that is needed to provide shear support low risk homes. This kind of bracing is often turned on its side and let into the stud framing (notching the studs) rather than being placed between the studs and further braced above and below. There are also newer versions that are T shaped pieces of metal (maybe 10' long but only 1" wide or so), where the base of the T is inserted into a small notch that is cut into the studs and the top of the T is nailed flat to the face of the stud.

Note that the other bit of blocking at the top of your photo appears to be for the knob and tube wiring, which I hope you're in the process of removing/replacing.

See also: What is a shear wall and what is it for?.

Wikipedia entry on shear walls.