fixing tornado damage
I agree, let it dry out as long as you dare.  When you do have to cover it up, get a tarp that is plenty large enough to cover the damaged area. A pic would be helpful. Get enough 1X3 cheap strapping and use it as a large washer with your tarps.  i'd try to go over the peak, roll the  edges of the tarp around the strapping and pull it as tight as possible and nail it down with 4 or 6d double headed nails.  Then take more strapping and install it perpendicular to the ridge line on 4 ft intervals.  This will help prevent wind from getting under the tarps but let water flow easily down the roof.  

Sorry to hear of you misfortune, glad to hear you and yours are OK. A lot of people we not so lucky in the last couple of days.