Since there's not much research that specifies one way or the other, it mostly depends upon your individual goals as which to do first: cardio or strength. If your goal is weight loss, they say cardio should be first, as to be able to be "fresh" to give it your all. If your goal is building strength, then doing strength workouts should be done first before you're fatigued and can lift heavier. If you do cardio right after strength training when you're trying to build muscle, the glycogen or muscle fuel becomes depleted. I usually like to do them on separate days, but if that's not an option, then go with the above method.
I don't think it matters whether cardio or pilates has a preferred time. I, personally, like to do cardio first just so I can say I did the "hard" workout first. Then pilates would be considered my cool-down after the cardio workout since it involves lots of stretching.