Try not to soothe your dog when he's extremely upset. It's sounds counter-intuitive, but soothing a fearful dog actually reinforces the fearful behavior. Tell him it's going to be okay and ignore the behavior (hard, I know!). I agree with getting a Thundershirt (has a similar effect as swaddling a baby), and also with getting the dog some calming medication.
Does your dog give you clues that a storm is approaching - pacing, panting, drooling, whining, etc.? We had a lab that could tell a storm was approaching up to an hour ahead of time (electrical changes in the air, I'm guessing). This was when we'd give him his medication, so that it was working when the storm hit.
Is your dog okay if you let him out of the crate? The metal of the crate may be conducting some electrical energy and making him nervous. Our lab liked to go hide in the laundry room until the storm had passed. We let him do this, not making a fuss over him. The smallness of the room gave him the feeling of a safe den, I guess. If you do allow him on your bed, do so, but don't comfort him. Just tell him that everything will be fine, then ignore.