[White Mustard; Sinapis alba alt Brassica hirta, B. alba | Black Mustard Brassica nigra | Brown Mustard, Indian Brown Mustard, Leaf Mustard; Brassica juncea]
Mustard Oil is the traditional cooking oil of Bengal (Bangladesh and the northeast coast of India) and is used for some types of frying throughout northern India. It is considered essential for reproducing the unique flavors of the regions where it is used, but in India, its use is declining because neutral flavored oils like sunflower are cheaper.
Like closely related rapeseed oil, mustard oil contains significant amounts of erucic acid, which was formerly considered dangerous. This has not been supported by recent research or by demographics (unless you are a male rat). Problems from human consumption do appear in times of famine when little other food is available. Apparently adequate amounts of saturated fats in the diet protect against problems from this oil, as well as from Canola oil (low erucic acid rapeseed oil).
More on Oils.
Buying & Storage: Mustard oil is easily found in markets serving an Indian or Pakistani community. You should purchase in a quantity you will use up in 6 months or so after opening. Store it in a tightly sealed bottle away from light and heat and with as little air in the bottle as practical. It is a fairly stable oil but not as stable as pure olive oil.
Cooking: Mustard oil is heated in the pan with no other ingredients until it reaches a temperature where the first wisps of smoke appear (about 480°F/250°C). Immediately take it off the heat and allow to cool to a more reasonable frying temperature (around 360°F/180°C) before adding other ingredients. This procedure removes the acrid taste of the raw oil and renders it quite pleasant.
Subst: Today, in India, mustard oil is gradually being replaced by cheaper but less stable neutral flavored oils like sunflower oil. I recommend, if you don't have mustard oil, you use pure olive oil (not virgin) or avocado oil, which are sufficiently neutral but more stable and with better health profiles than most oils. Do not bring these oils up to the smoke point.
Health & Nutrition: Mustard oil sold in the U.S. and the European Union is always labeled "For massage use only". I suppose you could use it for that purpose, but there is some indication that small children could be harmed by such use. Pretty much all that is sold is used for cooking.
The reason for this labeling is concern about the high erucic acid content which was suspected of causing heart lesions. This is now strongly doubted by researchers, who have also noted that demographics do not support this danger. Research done on rats is invalid due to a specific difference in metabolism. Mustard oil is, in fact, now suspected to provide some protection against cardiovascular diseases, and sufficient saturated fats in the diet apparently protect against heart lesions from this oil and Canola oil.
Mustard oil is high in the vegetable form of Omega-3 fatty acids (6% to 11%), which can, under some circumstances, be converted in the body to the more useful fish oil form. Omega-3 is fragile and is probably at least partially destroyed when the oil is brought to the smoke point.