Anybody who lives where hurricanes or tornadoes are a regular threat needs to know a little about emergency repairs.
Basically, what you want to do is cover the damage with a woven plastic tarp that is held in place with 1×3 wood strips. Here’s how I do it. First I roll one end at least twice around a long 1×3, then screw it to the undamaged side of the roof. The 1×3 “roll” should be against the roof so it won’t collect water and debris. The rest of the tarp goes over the ridge and down the other side of the roof several feet beyond the damage. Then I roll the opposite end of the tarp around another 1×3 and screw it to the roof sheathing, roll side down. Now it’s just a matter of using more 1x3s and screws to hold down the tarp’s sides. They don’t have to be rolled in the tarp. A “blue roof” isn’t pretty, I’ll admit, but it will keep the weather out until someone can repair the damage.
Having said that, this type of emergency repair is best left to someone who has the equipment and skill to do it safely. Roofs are treacherous, particularly when wet, and tarps are slippery even when dry. You don’t want to be wrestling with one in high winds, either. Better to submit a claim for property insurance than to have your family submit a claim for life insurance