What's the musky taste in curry?
If the flavor is so clear and overpowering to you, and you haven't noticed it in other dishes, it is most likely a spice (or another flavor agent), not some of the vegetables. There is no way for us to tell you which spice it is. The words people choose to describe smells are mostly arbitrary * so calling it "dark" or "musky" does not narrow it down. Similarly, "overpowering" and "unpleasant" cannot tell us which one it is - it is something that is pleasant to most people who eat curry (else it wouldn't be used so widely) and when you hate a flavor, it is always overpowering to you even when others may not even notice its presence. ** 

This means that the only person who can find out what it is is you personally. You would have to get a list of the possible "offenders", that is, the spices in a curry which tastes bad to you. Ideally you would be able to ask for the recipe for a portion which has the disturbing flavor, but if it doesn't work (restaurants can regard spice mixes as a trade secret), you can just look at popular curry recipes online and make a list of the spices appearing in them. The list will likely be manageable, maybe 7-8 spices in total. 

As the next step, try finding a way to smell each spice individually and seeing if that's what you hate. A supermarket won't let you open their spice bottles, but some oldfashione spice-and-tea stores measure spices out of the bag, or have them in a thin cellophane packaging that lets smell through. Or you can ask a friend who is likely to have Indian spices to smell them in their kitchen (if the person finds you silly, think twice if you need such a friend), or just buy a small amount of each spice somewhere - the money is not wasted, you can just start experimenting with Indian spices in your own cooking later. Prefer smelling the ground spice instead of whole grains or bark. If it is somethingn like fenugreek, you will find it out. 

If that process doesn't help you identify the spice, then it is likely to be something which needs to release its flavor. You will have to fry the ground spices in oil to see if that makes a difference for you. While you're at it, try finding a way to smell warmed mustard oil, that can also be a source of the smell you describe. 

I assumed here that you are talking about Indian curry, but if you mean another type of curry, just follow the same process but using the flavor process for another cuisine. If it is Thai, you might have to smell different brands of curry paste or some of the typical sauces (soy sauce, fish sauce) instead of individual spices. 



* I am excluding schooled perfumers and tasters here, they have a more standardized vocabulary, but everyday people cannot use it

** I never realized how frequently vanilla is used everywhere in food and cosmetics until I had a roommate who couldn't stand vanilla.