Sport is basically your normal driving mode most of the time while Strada is (like you said) for late night driving or early in the morning whenever you don't feel like causing a lot of noise.

In my Performante LP640-4 Corsa mode definitely feels and sounds like it's an extra level above Sport. I'm not sure if that's the case in a 580 as well but even standing still you can hear the slight sound difference between Sport and Corsa mode. Sport causes more crackles and pops which you hear and feel a little bit more in Corsa mode, at least from my experience.

Enjoy your new car, Tom!