All of them.
Chickens will nibble at anything. On plants like sunflowers, they aren't going to nip enough to cause much damage (to the plant), but if they nip too much on the potatoes, it could do damage to them (
solanine in potato leaves is toxic).
Chickens are more attracted to colorful berries and moving bugs than they are to green leaves, so you can use that to your advantage. If the potatoes get attacked by the Colorado potato bug, the chickens will go through and clean off every last bug before they would start nipping at the leaves. I have a goodly amount of wild strawberry growing everywhere, and if I let my girls out to free range, that the the first thing they will go for -- well, unless I turn over a board that has a a lot of slugs on it.
You can chop up green tomatoes into bits and chickens will eat that, but they usually leave green tomatoes alone. As soon as they turn red, chickens will make a bee-line for any ripe tomato they can find. Corn is a problem for chickens, because they don't have fingers to strip off the husk. If they did have their fingers, then there would be one less menu item at Zaxby's. Similarly with watermelon, a green one on the ground they will pass up. But cut it in half, and they won't leave it alone until there is just a thin sheet of the rind left.
Sweet potato vines make good chicken fodder, but it is not one of their favorites. At harvest time, I usually pile up the sweet potato vines and run over them with the lawn mower before I empty the bag in the chicken pen, then they find lots to pick and scratch at.