Serious case of herbicide damage. Probably 2,4-D.

Take steps to rule out contaminated organic matter such as manures or compost. Do a bioassay as explained on these pages.
http://puyallup.wsu.edu/soilmgmt/Clopyralid.html

Here is a link that might be useful: rule out clopyralid

Thank you Jean! Based on your response (and other research I've done on the web) and the fact that our local feed store also suggested herbicide damage, I think the problem is due to the fact that we used composted manure from my husband's cows when we planted the vegetables. He grows the grass/hay that we feed them and he confirmed that he uses weed killer to control weeds before cutting and rolling the hay. (Makes me rethink eating any beef other than organic beef, that's for sure!) Any suggestions for how to fix it? I saw something online that said the person cut off the damaged parts and fertilized to encourage healthy new growth.

The pages I linked you to have all the info you need.

- To verify the manure was the source, do the bio-assay.
- The damage won't be reversible.
- The plants may or may not grow out of the damage. It depends upon the "dose" of the herbicide.
- If the herbicide is clopyralid or one of its close relatives, it exits the animal intact.