Appears the furnace is allowing exhaust fumes into the house. That is real bad. A crack in the heat exchanger is a possible reason for the smell. Even though it was just serviced, have it looked at again. Many times, without someone mentioning a problem, the service tech will not find a broken heat exchanger. Only when the heat exchanger was really bad (split, burnt out) was when I found them. Be sure the chimney is not plugged either. Don't put any faith in those monoxide testers, they routinely give false signals and sometimes, don't work at all. Been there, done that. A properly working oil furnace doens't put out monoxide anyways, so don't bother buying another detector...just get your furnace looked at NOW!.
Originally posted by smoomlk
...I noticed the other day that there was a smell in the house when the furnace was running. It is hard to explain but was like burning oil. It was very heavy and made me feel kind of sick. I had a functioning monoxide tester working and it did not signal anything.