From Thangam Philip’s book Modern Cookery:

Mustard seeds (Brassica nigra) :
Hindi – rai
Tamil – kadugu
Telugu – avalu
Kannada – sasuve
Oriya – sorisa
Marathi – mohori
Bengali – sorse
Gujarati – rai
Malayalam – kadugu
Kashmiri – aasur

A recent discussion with Lalitha Sankar and Prasad Santhanam brought up this linguistic diversity. Clearly sorse/sasuve/sorisa/ come from the same root as sarson, which are mustard greens. Maybe aasur is derived from that as well, but where do the others come from?

It turns out that the Farsi word is خردل, or khardal (thanks to Amin Mobasher for the help), which is probably the source for the Tamil/Malayalam.

But, much to my chagrin as a Maharashtrian, I do not know the origins of mohori, nor do I have any in my kitchen right now (soon to be rectified by a trip to Devon)!