In the image you included it's difficult to say exactly what the black spots are but more importantly where they are. We'll presume that the diagnosis is correct (oil, and uncleanable) but is it on the sensor or the low pass filter covering the sensor?

If you feel brave, stronger, cheap, or a risk taker you can look at this set of cleaning instructions from cleaning digital cameras and compare the advice with other sites to verify the suggested methods. You can also try sites like LifePixel which replace scratched low pass filters (for that camera) for U$250. Looking on the Internet for a replacement sensor (with LPF) it's going to cost under U$120 (without labor). There are videos available showing sensor replacement if you're brave and have nerves of steel. None of the above DIY is "recommended", but it's possible.

It's also possible to take a photo of a white card and use dark pixel correction to fix every photo you take, it's a question of what level of perfection you want and how much time and money you want to spend. A little use of the "Healing Tool" could fix that photo in a half minute, then it comes down to "how often do you use your camera?".