In Tamil, these roots are called Senai Kizhangu, Cheppan Kizhangu, Karunai Kizhangu respectively. 

Elephant Yam:

Senai Kizhangu is called Elephant Leg Yam in English. It is the common name for some species in the genus Dioscorea. It belongs to the edible root type.

It looks like this. It will not be mashy, or pulpy. It can cause slight itching on the tongue. It has to be cooked very properly to avoid itching the tongue. It is said to be good for hemorrhoids.

This Elephant Yam is a little hard to cook. First, soak the skin in water, peel off it, and then soak it in a little sour/tamarind water to prevent itching. Then cut it into small pieces and wait for the water to drain completely and make your recipes.

No one would say it is so delicious

Colocasia :

Scientific name: Colocasia

Type: Genus

High Classification: Arums

Sequence: Water plantains

Looks like this. It will not be mashy, or pulpy once cooked. 

Seppan Kizhangu is the choice of a lot of people. Put it in water for a while and clean it to remove soil. Add a little bit of salt and cook for 5 minutes. Remove the skin. Once cool down, add oil to a pan and add mustard seed, urad dal, and Little channa dal. Once the mustard starts to splutter, add the cooked roots. Add a little bit of masala powder, turmeric powder, and salt. Sprinkle a little bit of tamarind water on it.  Once starts frying the color will become a golden color. Now again add another two spoons of oil and fry it. Sprinkle some curry leaves now and serve it with Rice and Rasam. Now, you will feel the real taste of Colocasia.

Amorphophallus paeoniifolius:

Amorphophallus paeoniifolius is another type of root. It will make the tongue itch more.

Cooking this root is a kind of punishment. Sometimes, You will feel itching in your palm as well if it is freshly harvested. It is better to choose roots that are harvested many days before. But, it is very good for the body among the three. It has to be handled with patience

Name of these roots exchanged in certain areas of India, particularly in Tamil Nadu.

During the Pongal festival every year, People used to buy mostly all the tubers for making curry.