What are your goals?
What do you want to know from tracking your fitness? What do you want to be able to look back and see? What do you need to calculate?
As the PP said, calorie burn from ST is minimal anyway. Calorie burn isn't why we do ST. So yeah a generic entry for the total time spent would be fine.
Unless you want to look back over what sets/reps/weights you used to do. In that case you do need to enter each exercise individually to specify those values.
Do you mind if I ask why you use over 20 machines? What are your exercise goals? What are you trying to achieve? There are four exercises that work your entire body, and if your goal is general fitness, health, weight loss, rather than perhaps body building, there would be no need to ever do more than these four exercises. Over 20 would imply you're probably doing a lot of isolation moves that engage one small muscle at a time, which are generally not very helpful.