Lots of them. Not a lot, a little, after all, we all need a little iodine or we'd die. But to find out exact amounts, you'll have to do further research than me. Wheat grass isn't wheat, it's the first grass that rises above the ground when wheat is planted, then that dies, another shoot appears, and from that wheat grows. So wheat grass shouldn't bother you. If you're still afraid of it, barley grass is also great, but you can't find it fresh, you'll have to either sprout it yourself or buy it in powder or pill form. Wheat grass you can find fresh and organic.
I am allergic to wheat so I'm not sure if I can juice wheat grass. On the thyroid problem what veg have the iodine in them I am new to this.
The best things to juice are colored vegetables, such as kale, collards, broccoli, carrots, sweet potatoes, parsley, dandelion greens, and such. But be careful with your thyroid, some of these might present an iodine problem. I would stay away from too much fruit, too high a sugar content, which is inflammatory. And as laura said, if it's not organic, better to not juice. It just concentrates the amount of pesticides you get. Best thing to juice: wheat grass.
Juicing can be a good addition to your other treatments and protocols. My favorite is organic apples, with organic carrot and a little organic celery. Make sure all fruits and veggies are organic though.
Did you mean plant and animal enzymes? Good stuff!