In my experience..
Hold off:
1 - To prevent an attack. You prevent someone from coming at you by stalling them or putting up barriers so they don't move forward.
2 - You delay making a decision or taking action until the time is right.
3 - When you wish it would not rain, example: I hope the rain holds off until I get home
Hold up:
1 - You stand in the way of people and stop them from going ahead or sticking to a schedule.
2 - You hold a place up means you rob it.
Hold over:
You keep something happening beyond the time it should. Like a film at the cinema. It was such a box office hit that they hold it over for one more week.
I hope it helps