Storms, especially those with high winds, can destroy landscape trees. You will need to assess the damage to see if the trees need to be removed.
A common issue with older trees is that high wind cause the trunk to literally split down the center. This can happen if a tree already forks low on the trunk, but it can also happen to single trunk trees if a large branch breaks free and pulls part of the trunk with it. In most cases, it is best to have the tree removed because it likely won't recover from the split. If it does recover after one section of the tree is removed, it will have a poor, unattractive growth form. In rare cases the split can be splinted back together, typically by bolting, but this is usually only done for minor splits.
A combination of high winds, saturated soil, and a top-heavy tree can cause the roots to begin to heave. After the storm passes, you will notice that the tree is now leaning and that the soil around its base looks churned or disturbed. If ignored, the next storm may result in the entire tree blowing down. In some cases the tree can be staked or anchored. This, combined with pruning to minimize the weight of the crown, can keep the tree from blowing down. In other instances, such as when disease is weakening the roots, it may simply be safer to remove the tree.
Major Branch Loss
The loss of a few branches is no reason to remove a tree, although it will need to be pruned to remove the deadwood and more safely balance out the weight in the canopy. The only concern is if the branch loss primarily affects one side of the crown. If most of the larger branches are ripped off on one side by the wind, then the crown can't be safely balanced. This makes it more prone to blowing down under its own weight.
A bit of bark damage can occur during a storm, either from branches being torn off or items blowing into the tree. A few strips of missing bark aren't usually a concern, although your tree service will likely clean up the wounds so they heal cleanly. The only time you may need to remove a tree due to missing bark is in the event a bark strip is torn off that completely encircles the trunk. This is called girdling, and it effective cuts the crown off from the roots. This will kill the tree.
Contact a tree removal service, like Pete & Ron's Tree Service, Inc. or a similar location. They can assess your tree and determine whether the tree can be saved or if removal is a better option.