So this is what I am getting, even with different lenses. I'm assuming this is not dust (?) since using the in-camera sensor cleaning command didn't change anything. Or is it possible that it IS dust that is simply stuck to the sensor? Is the oil pattern that is reported to show up on the right hand side of the image some hard-and-fast rule when it comes to ruling oil in or out? Clearly the specks are evenly distributed on the sensor. in June, less that one year after purchasing the camera, I've started noticing the larger specks in the tops of my images mostly because they are against a bright sky, but there seem to be a lot of them all over the place. What do I do next in terms of diagnosing the problem? I can tell you I am not comfortable cleaning it myself.
It mostly looks like dust to me. The in-camera sensor cleaning feature can only remove loose particles.
First get a good blub blower. The Giottos Rocket Blower is highly recommended. Use that to try to blow the dust off of the sensor.
If that does not work then the sensor need cleaning. If you are not comfortable doing it yourself then take it to a good camera store and see if they can do it. If there is no place to take it locally then you can send it to Nikon.
I agree with the other posters that this does not look like the lubricant spots I had. You might remember to hold the lens opening on the camera in the down position when using the rocket blower and do raise the mirror for cleaning using the utility in the "settings" menu. Then you could study up on wet cleaning and learn to do that yourself. It really is easy. Nerve-racking the first couple times, but easy to do.