“I hate getting phone calls during ‘off hours/ after hours/ off-duty hours’” Which one is correct? Off hours VS after hours VS off-duty hours

All are correctly used, in my opinion, but my preference is after hours and you probably wouldn't use the word During. I hate getting phone calls after hours. I use that at work all the time. off-duty seems like it would work better if you were working in the military or police, or another job that could be described as being on duty. Also, I don't know if I would use the phrase "off duty hours," just "off duty." I work with virtual servers, I don't really consider myself to be on duty. It wouldn't be incorrect to use on duty/off duty, but for me, it sounds like it's making my job seem more important than it is. In your example, I would say I hate getting phone calls when I am off duty. Off hours gets the point across, and I think it is equally correct. I just don't hear it used as often in my own experience. I might use it in a different context. If someone at my job wanted me to patch their servers, I would say that activity would need to be done off hours (or after hours). Off hours sounds good to me when it's used as an idea, and not my personal hours. This is all subjective, and how I use the words. That is why I say they are all correct. It will come down to what people prefer to say. If the people at your job say it one particular way, go with that.

Either "I hate getting calls after hours" or "I hate getting calls *during* off-hours / off-duty hours". In other words, *not* "I hate getting calls during after hours."

I would say "out of hours" but that could be a British English thing.