Don't know about Yams (Dioscorea batatas ) as they are a tropical plant. Most references are to the use of the roots. Vines of the sweet potato (Ipomoea batatas) are edible and popular in Asia. Like every thing else young tender leaves and shoots are best. Irish potato leaves and stems (Solanum tuberosum) are mildly toxic. Don't know anyone who has tried them but they probably taste bad.
21. Potato (Solanum tuberosum) has tubers that are great to eat but the leaves have a lot of slightly poisonous alkaloids in them. This is the case with many plants in the nightshade family (potato, eggplant, green pepper, tomato). In some countries, varieties of potato have more alkaloids in them than are allowed by law in the U.S.A., and green parts of these kinds of potatoes can make one pretty sick if eaten. http://www.sciencebuff.org/some_poisonous_native_and_cultivated_plants.php