To check for sensor dust/oil spots you can run a simple test. Using Aperture Priority mode, Matrix metering, ISO 100 and the smallest aperture the lens will allow (e.g. f/22), point your camera at a clean white surface, like a sheet of blank copy paper or a white painted wall. You want to fill the entire viewfinder, corner to corner, with this white paper, wall, whatever. You can also aim it a clear blue sky if that's easier. Once everything is set, take a shot. Open the file on your computer and review it at 100%. Scan it from corner to corner looking for dark spots. If you have Adobe Photoshop there is a function in Adobe Camera Raw called "Visualize Spots" (Spot Removal Tool) that will make this easy. Lightroom might have a similar tool but I don't use Lightroom so I wouldn't know.
I'd be happy to look at your test shot as well, if you want, but I'd like to be able to see a full-size, JPG (meaning it was shot with JPG settings of "Large/Fine") straight out of the camera, or a RAW file; either will require uploading the image file to Dropbox since the forums won't allow you to upload file that large.