There's probably a couple things to do - and many have offered great suggestions. Basically, it sounds to me like it needs to be addressed both mentally and physically. Poor little kids shouldn't be stressing like this at that age.
We were always given ginger ale to sooth our stomachs too. I know some stores sell small glass bottles of Schweppes or cans of Canada Dry. I'd keep some of these in stock - as well as some saltines.
Also, try to find ways to help sooth her. No, we can't prevent tornado's, but we can have a "preparedness plan" so we know what to do if one might come around. It might be time to consider therapy, or maybe writing in a journal, or even some activity that will help calm her down. OR even find a stuffed animal that she can carry around with her when she gets nervous.
I've noticed that my 5 year old - before she goes to sleep, I go in her room with her, and we get settled into her bed - and we just talk for a few minutes about whatever is on her mind. I'll tell her I "Love her love her love her", and about some things she did that were really great that day - that she did a good job. She'll tell me the "whole story" which includes "having good good dreams and snuggling up in the bed." I only stay in there for about 5 minutes - enough for her to get past the "fidget and wiggle" stage and actually get almost asleep. But all of that helps her have a good nights sleep.
For what it's worth...