Area and field are not exactly the same thing: for example economy is considered a field, so like let’s say a discipline, but then area is something like “economic growth after a recession” is an area which is more like a topic. In the second case, field doesn’t work. Sphere on the other hand has a sociological meaning; look at this example: During the 18th century, thanks to the growth of printing industry, the public sphere extended dramatically and more people started engaging in political discussions. James Madison, in Federalist Papers, famously uses “sphere” to talk about the “active people in the society who take part in the process of decision making.” Hope this helps

The answer to the question, "Where do you work?" would be the name of the company, or its location. If the question were, "What area/sphere/field of sport to you work in?" then you could use one of those terms in your answer. "Sphere" sounds a bit more formal to me. The other response didn't make much sense to me.