A furnace that gives off oil fumes usually indicates that the system requires maintenance. The oil fumes do not pose a risk, but point to a crack in or a misalignment of the oil burner.
When an oil burner is lit, it causes pressure to build up in the combustion chamber for a short period. Any smoke from the oil that is not burned can travel to the fresh air chamber and flow through the house. A repairman from the oil or furnace company should be able to remedy the problem. Fumes that do not have scent are the most dangerous because they are caused by emissions of carbon monoxide.