The actual pathway? I can get into a lengthy explanation but the short answer is, nobody really knows. Hormones affect the brain and we know so little about how or even why the brain works. And yes, strength is, to a great extent, nueral, which is why the old timers used to use cycles to prove that they could lift more weight -- even once they got off. Today, it's different. No sauce, big loss.
There is also a physical component to testosterone also -- mainly ATP and blood volume. Of course, using creatine and BRIDGE could cover that pretty well also. And muscle tissue absorbs nitrogen more efficiently making them bigger, thus stronger. Using GEAR fills that gap. They really are a great advantage to the guy to wants to used steroids sparingly and make continual gains.
As for the libido effect, I'd say that's very primal and instinctual. Testosterone is the driving force and we're designed to procreate as much as possible until we get eaten by the saber tooth tiger or killed by a younger tribesman with more testosterone.