Thank you for your kind answer, Xcalibur.
Living and learning, great to have people like you in the forum, sharing experiences. I did perform your test and, to my surprise, several spots that I ordinarily don't see in my pictures appeared all around the frame!
But none of the spots is larger than a few unit pixels: they are really small, and have irregular shapes, appearing like textbook sensor dust. One is actually a very distinguishable hair from my cat
Yours, on another hand, look very serious and concerning indeed, I insist that my "sensor dust" looks totally different than your "oil spot".
In the D7000's defense, I change lenses *very* often (I always appear to be with the wrong one

, and not always in the cleanest environments (beaches, Rock and Roll concerts, back beds of *moving* pickup trucks, weddings, parties, you name it), to say the least. Add that to the fact that I own six lenses (not including borrowed/rented ones), and that my D7000 is close to 50.000 pictures (it is so old that came with the very first firmware), and I have to confess that I'm not surprised at all that my sensor is a little dirty.
But IMHN that my sensor dust is actually so small, that I'm not sure I'll risk cleaning it myself, although I do have a gentle airbrush, and some hand ability. Will probably wait until it gets dirtier, and then send it to a specialized workshop.
Would you please keep us posted about what solution (if any) you found for your oil spot? Man, we do learn from others' experiences!
Thank you very much,
Paulo Feitosa - Curitiba, Brazil.