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)!
An Ergodic Walk 
Do you know what is the origin of “rai”?
It’s probably from “rajika” and refers to mustard seeds being used as a unit of measure for gold.
In fact, “mohori” in Marathi may also come from the same meaning — mohor refers to gold coins, and so mohori could be derived from that as well.
As we discussed over Thanksgiving Break, mohor is a coin, usually gold, and the name of the Indian gulmohor tree with its flame-red flower (gul = flower (Tangul = flower that blooms in the evening), from the Turkish and possibly Arabic or Farsi as well, and mohor = red gold?) supports this possibility. Wikipedia mis-states that mohor = peacock, and especially since the color of the gulmohor is quite different from a peacock’s colors.
Mohor is also a Nepali word for money. In Farsi I think it means “moon” so that is probably not the origin.
Now that you mention it, there is also a Bengali word “mohor” which means money. It’s considered a slightly old-fashioned word in the sense that its not used in conversation, only in literature.