1967 Cadillac Deville Car/Exhaust Odors in Garage

I have a 67 Cadillac that has strong exhaust-type odors when parked in the garage. The exhaust from the car when running is very heavy (but no visible smoke or burning oil smell) and some of the odor could be residual from parking the car. But, when I drive the car and park outside, nobody notices odors on their clothes, but after garaging everyone who was in the car reeks. The car while parked in the garage also smells up the whole garage. It doesn't smell like raw gasoline, but does smell fuel-related and much like the exhaust.

Many people have told me that all old cars with carburetors will have a strong smell when parked and a stronger lingering exhaust smell when running. Is this true or should a properly running engine be relatively odorless, especially when parked and cold? What types of problems should I have a mechanic investigate?

Thanks!