As has been mentioned, none of them are exclusively "Indian", although they are of course used in dishes from that sub-continent. Have you not seen them in Chinese/"Asian" groceries as well?
16 hours ago, Thanks for the Crepes said:Today I was in an Indian grocer, and ran across this vegetable not for the first time. Does anyone know how to cook it, or some great recipes?
It seems to be available pretty much year round. They finally had a sign with the name and price, which was dudi at 99 cents a pound. Google corrects me to dudhi. Is it squash?
Commonly also known as opo squash a.k.a. 浦瓜 (pou4 gwaa1) as the Chinese name I know it by, with various other names for it around the globe also. Closely related/a variant of "fuzzy squash"/"fuzzy melon", which I have also posted frequently about (just search for "fuzzy squash" on eGullet). I buy both from my usual Chinese grocer and cook them similarly. I find opo squash to be more spongy in texture than fuzzy squash. I cook them in soups commonly, sometimes stir-fries; or, rarely, stuffed. I've posted about opo squash on the grocery topic several times; and shown some soups I made with it on the cooking topics - e.g. here, here, here (scroll down). There are others.
16 hours ago, Thanks for the Crepes said:I can also get this
As has also been mentioned, a widely used vegetable in E and SE Asian cuisines also. See the wikipedia article (embedded link above) for its many names. I've talked about this (a.k.a. 勝瓜 (sing1/sing3 gwaa1) (or also, 絲瓜 (si1 gwaa1); a.k.a. "angled loofah" and other names) on the grocery thread several times (see here for an example; scroll down); and also on the cooking threads repeatedly. I like this in soups, and occasionally stir-fries and a few other rare ways (for me). I usually take the ribs off (with a potato peeler; done in a minute or less) before slicing up and cooking. See here (scroll down), here, here, here, here for soup examples; and here, here, here for stir-fry examples.
16 hours ago, Thanks for the Crepes said:and this
Yes, bitter melon, as others have said. This variety, however, is one that I (personally, perhaps) associate more with - yes - "Indian" dishes or "Indian-influenced" dishes (including in SE Asia) than with E/SE Asian Chinese-influenced cooking, although it is not unknown. The variety of bitter melon used in the latter cuisines tends more (in my experience) to be the much larger, less-convoluted-ridged cousins of the variety you ask about. The one you post is generally around 4-6 inches in length, whereas the more common varieties used in Chinese/Japanese (and associated cuisines) tend to be, say, 8-14 inches in length and much lighter green in color, like the ones another poster above exemplified in a dish. (See here, too, for example) I dislike this "Indian" variety myself. It's much more bitter than its larger cousin. I don't think I've posted about the "Indian" variety here, whereas I've posted about the larger variety here on eG including the commonly-done beef & bitter melon stir-fry dish.