I have a new house with a forced hot air oil heating system, and after having lived in it for only a few weeks I've noticed that there is an oil odor that is permeating the entire house. The odor is coming through the heat registers when the furnace fires.

What could be causing this, and how is it fixed?

Have you looked for oil leaks in or around the unit? If the house is relatively new, I should think some type of warranty coverage would apply. The installing contractor usually provides 1st year labor as a courtesy when problems arise. I would advise you to give them a call.