You have a couple of possibilities. The heat exchanger could have a crack, between the fire pot and the hot air duct side. Or, the chimney could be low on draft, allowing some of the ignition fumes to come out through the barometric damper or elsewhere. ???

In some cases, you can check for an exchanger crack, by turning the blower fan on and feeling to see if air is blowing out the fire (burner) inspection hole.

Did you watch as the thermo calls for heat
how long it takes for the fuel oil spray
to ignite? On most burners the control unit
times out in 1 minute. 50 seconds
of oil spray and a delayed spark will
give you a oil smell and quickly go away.

Have you had burner adjusted?

tmajor, fire pot? You must have your mind on stokers.

"50 seconds of oil spray and a delayed spark will
give you a oil smell and quickly go away"
I don't think so corvetteguy,, first off the primary control only has a 45 second time out at the most and if you sprayed oil into the chamber for that long before it ignited you would definately HEAR something before you smelled it. And the smell of a delayed ignition doesn't go away the quick either.

For the last few years, the Beckett primary controls time out at 15 seconds.

50 seconds of oil followed by ignition will sound like a runaway train ride.

I would have burner tech check operation, test ignition
transformer.
I find a lot of Heat Exchangers burnt out because of
improper duct sizing.
If you are getting odor from registers, I would be very
suspicious of exchanger.

Well a call to the heating and cooling company resulted in the following response: "It's normal to smell oil from an oil furnace." So...yea...Anyways, I checked the draft going out the barometric damper--I used a lighter near it and the flame was drawn toward it. The furnace is serviced annually by the heating and cooling company (service contract). Also, I want to emphasize that the smell is not constant, and does not happen every time the furnace comes on. It happened once before Christmas, and once the other night. The furnace isn't very old either--it was installed in late 2001. It has a Beckett burner.

I don't think its been established yet here if its the odor of oil he smells or the odor of combustion. Or for that matter where the smell is coming from, the basement, the registers, etc. and when exactly its happening. We used to get calls of oil smells shortly after the customer got a fill up. My past experience here tells me that smells are the most difficult thing to help diagnose in a help forum. Boy somebody could make a fortune if they developed smellware!

The smell comes out of the registers throughout the house AND the basement smells. I figure that the furnace might be pulling in the smell in the basement and distributing it throughout the house. I do not know what the exhaust smells like, but I am familiar with the smell of the oil, and that's what this smells like. When this happens, the smell is strongest near the tank, not near the furnace.

Do you see any broken tank vent pipes or oil on the floor?

Lots of things can cause a faint oil smell. Nozzle after-drip (Not as common on burners with pre-purge, post purge and oil solenoid valves), delayed ignition, puff back. Misting from loose fill, vent and gauge tappings/gauge glass. Weeping threaded fittings, flare fittings, firomatic valves, filter housings, pump gaskets. Few service techs and installers crank fittings tight enough or make perfect flares.

As I said before, no oil on the floor or broken pipes visible.