I haven't heard a 'hold over' in that sense, 'hold off' is more common to mean 'delay'.
Hold off, put off, postpone and delay are all very similar, they all mean to do something later than originally planned.
Hold off (on): (when we mention a verb after, we use the structure 'hold off on ___ing')
I wanted to talk to him, but I saw he was busy, so I decided to hold off. I will talk to him later.
You should hold off on calling the doctor until you get your medical results back. (Wait until you get your results back, then call the doctor. Don't do it now.)
Put off: (this can mean to not do something, or to make someone not want to do something)
I really need to finish my essay – I keep putting it off. (Every day I say, 'not today, I will do it tomorrow')
The film 'Jaws' put a lot of people off swimming. They were scared by the movie, and they didn't want to swim after watching it.
Postpone:
I know we agreed to have coffee this afternoon, but can we postpone till tomorrow? I am busy today.
The boss is sick so we need to postpone the meeting.
Delay: (this is like postpone, but can describe actions that are out of our control)
The weather is really bad, and I think it will delay our flight. (even better: I think our flight will be delayed)*
If you don't love her, you need to break up with her. Stop delaying the inevitable!
*A flight can be delayed or postponed, but if it is DELAYED, it will still happen today, just a few hours later than the original time. If it is postponed, it will not happen today. Maybe the airline will give you a ticket for a flight on a different day.