I would use the Q-tips every day for awhile. Plus, before every sewing session, I would sew at high speed for several minutes. You can take the needle out and drop the feed dogs to do this. I would place some white fabric between the feed dogs and the presser foot and lower the presser foot before doing this. That would allow you to see any specks of oil that might come flying out. Sounds as if the machine was over-oiled. It can take time for all of the excess oil to respond to gravity.
Also, I am wondering if he used sewing machine lubricant (squeezes out of a small tube, white, but with a similar consistency to vaseline)? This is what should be used between gears, instead of sewing machine oil. If he only used oil, that could explain why you are getting flecks of oil when you run the machine. Here is a link to the lubricant (which is used *only* on gears):
http://www.amazon.com/Vogue-Fabrics-...dp/B008EUCSKS/