No, mustard oil is not soluble in water.
Mustard oil, like many other oils (such as kerosene and coconut oil), is insoluble in water due to differences in polarity. Water is a polar molecule, meaning it has a slightly positive and a slightly negative end. Oil, on the other hand, is largely nonpolar, meaning its charge is evenly distributed. Polar substances tend to dissolve in polar substances, and nonpolar substances tend to dissolve in nonpolar substances. This principle is often summarized as "like dissolves like."
Because water and mustard oil have very different polarities, they do not mix, and the mustard oil remains insoluble. You'll observe this if you try to mix the two; the oil will form a separate layer, demonstrating its insolubility.
