Build it tight & vent it right! This is the rule to build by.

Seal off air infiltration from the exterior of your home, tightly, no air leaks in or out. This includes vent fan back draft dampers for kitchen – bath – dryer exhaust fans etc, window & door weather stripping, fireplace dampers and glass doors, attic scuttles, attic fans through the ceiling of the house and all gaps around wall penetrations for electric wires & light fixtures. Make the exterior envelope as tight as possible. Replace gas fired furnaces and water heaters with sealed combustion system models so their combustion air comes into the combustion chamber or the appliance instead of sucking into the house through drafty windows and doors.

Then vent it right which means optimally 1.5 to 2.0 air changes per hour for the entire house. Less than that is unhealthy as we need fresh air from nature for oxygen. More than 2.0 air changes per hour air is an indication of too many leaks in the building envelope resulting in an uncontrolled environment, wasted energy, cold and drafty feeling house in the winter, dusty environment, etc.
Seal the damper AND balance your ventilation HVAC system.

The negative pressure situation must change or you will continue to fight Mother Nature. The laws of physics (Mother Nature) seek to equalize pressure imbalances; all of nature is trying to correct negative pressure towards equalizing the inside of your house. Yes, you must tightly seal your damper, however, the air infiltration draft may move to another part of your house without a smell. Same problem, less smell.

The disease is the unbalanced pressure in your house, maybe from your HVAC system, maybe from your vent fans, maybe from a big commercial exhaust fan in the kitchen, maybe your clothes dryer – on and on. Or it can be a combination of all of the above.

The likely solution is adding more return air registers and ductwork to your HVAC system. Most forced air HVAC systems have grossly undersized air returns.

Imagine adding more properly placed return air capacity to your HVAC system so that the supply air will exhaust and draw back through and into the furnace ductwork. This will result in less air being drawn down your chimney. Sealing your damper is very important, then balance the air pressure for real success, comfort, and health.