If any of the branches were bigger than an inch or so in diameter, it would be good to have the stubs that were left on the tree trimmed so that they do not allow water into the trunk. Large branches can leave large wounds that cause the trunk to rot, and then the tree falls over in such high winds.
If only small branches fell, then next spring look at the tree and you will see more small dead branches. Any time of the year is a good time to remove dead wood from a tree. A large number of branches falling from one tree may mean it is overdue to be thinned out so that more light makes it through to the inside.
Large branch pruning should be done this winter. Any large stubs and any branches that are not fully broken, but are hanging on, should be removed.
Hire a licensed arborist to clean up storm-damaged trees. I have seen trees being topped by ignorant tree pruning companies. Cutting off the ends of every branch on the top of a tree results in more maintenance and less safety. It creates the weakest possible branch attachment, the exact kind that breaks apart in storms.
The first thing to do is clean up the wound to see how much trunk is left in good condition. Use a knife or saw to trim the ragged edges of the wound. Remove as little as possible of the good wood. Do not coat the wound with any black stuff or paint; research shows that all these coverings slow the healing process.
The remaining trunks may need to be bolted together for support. This will require drilling a hole through the trunks. A threaded rod is run through the holes. Nuts and washers at each end hold the trunks together. Cables higher up that have adjustable nuts also offer support for narrow trunks.
The bolts and cables are very useful to prevent trunks from splitting. An arborist should be hired to install these devices. Putting them in the wrong location could split the trunks.