Do you ever train both power and strength within the same training session?
Yes med ball, plyometrics and sprinting is power work, whilst weights is strength
Not really. You can do power or strength speed work, edurance work, speed strength work, etc with weights…
Depends on your definition of a training session for me 1 day is a session speed or speed endurance then, med ball then, plyometrics and then weights so yes you do train them in a day which equates for me to 1 session since the breaks between the components are not long enough for us to consider as seperate sessions.
Speed work is a form of power work. Med ball is power work, plyometrics is power work. Weights is strength work.
Speed-strength IS power work under speed strength there is two types of power expression reactive strength (box drills hurdle hops). Or explosive strength jump squats and bounds. Reactive strength is form of plyo with GT equating to <140ms explosive strength is any plyo equating to 160ms and upwards to circa 300ms. Strength speed (cleans and snatches) occupies 300ms to 1 sec. If it takes longer to apply force to the ground then it is probably more strength than power.
So the answer is yes emphatically. Do not take my answer for it watch the great man’s DVD read his E-books its all there (the order of work to be done on a speed speed endurance or special endurance day).
You can do speed, speed-strength, strength-speed, strength all in a session (a session being 1 day of training).
I think ltruett might have just been saying that you CAN do power work in the weightroom and weights are not just necessarily strength. ??? 
yes, I do olympic lifting(cleans and snatches) followed by squats and or pulls. power and strength in the same workout.
Rob