RR, Here is the definition of VAM and the formulas for calculating Watts/kg from VAM and and % grade.
http://en.wikipedia.org/wiki/Mean_ascent_velocity
You are not inconsistent. It is Strava that is inconsistent in its power calculation. Strava does not measure power but calculates it. I know one of the Strava guys so I will ask him how they do it. Wind and road conditions influence how much power is required to move a bicycle at a given speed as well as rider body position.
The good thing about VAM is that cyclists tend to climb the same hills so that the road and wind conditions are similar. And rate of climb is what racing is about.