PrP: The water service has been shut off.
PaS: The water service was shut off.
PrS: I have the water service shut off. (is it correct?)
Present perfect works with the above sentence, "The water service has been shut off", but DOES NOT work with your first sentence since you specify a specific timeframe. It would be incorrect to say:
"This morning the water service has been shut off". (incorrect)
If you want to indicate that it happened this morning, you must use simple past:
"This morning the water service was shut off". (correct)
If you don't specify a time frame, then either of them are right, i.e.
"The water service has been shut off" and
"The water service was shut off" are both correct.
Your third sentence isn't formed correctly. It would have to be: "I had the water service shut off", but this only works if you arranged for the water service to be shut off. In the other two sentences it doesn't say who shut it off. That part is left ambiguous. I would therefore, avoid this construction here unless you were the one who arranged for it to be shut off.