When an astronaut walks on an asteroid, how much would it alter the asteroid's rotation?

The effects that the landing and the "walking around" impose on the relative motion of the asteroid depend on the amount of force or torque being applied by the astronauts and on the m and moments of inertia of the asteroid. It is a basic problem in mechanics that can be solved by the application of Newton's laws. Once the motion is altered, it would remain in the altered condition until another force or torque is applied, whereupon a new solution would have to be obtained. The process is really pretty straightforward, although not trivial. It is in fact identical to the way that we predict how much propulsion is needed to maneuver the spacecraft to get it there in the first place. Same equations, same methods, just more m and moment of inertia.