Severe thunderstorms frequently come with hail, which is unlikely to seriously injure you (unless its really big) but may be quite painful. When on tour, I carry a tarp to use as a groundcloth for the tent, but I always strap it to the outside of my panniers - when I have to hunker down in a ditch, it helps to have something to put between me and the rain/hail/ditchwater.

Sometimes highways have relatively high embankments, and these are better than ditches for shelter - you can get down below the level of the road, but still be on the slope instead of the bottom of the ditch where dirty water pools.

On the plains, thunderstorms sometimes spawn tornados as well; the solution to that is to get as low as possible in the ditch and try to move away from trees, cars, cows, and any other large objects that might get thrown at you.

Those tips are for situations where you can't find shelter, but don't be bashful about asking random strangers for shelter - people in areas prone to thunderstorms are aware of the danger of severe weather and are unlikely to turn you away if it is really bad.