"So, the fumes are either migrating through the floor or the furnace is drawing air from the garage, which is more likely?"--- Could be both. If the joints are not taped for fire-stopping in the ceiling of the garage, or the fumes are entering through gaps in the intake ducting below the furnace. It could be drawing part of the supply air from the garage air, which is very dangerous.
Electric furnaces are more expensive to operate than other electric resistance systems because of their duct heat losses and the extra energy required to distribute the heated air throughout your home. Heated air is delivered throughout the home through supply ducts and returned to the furnace through return ducts. If these ducts run through unheated areas, they lose some of their heat through air leakage as well as heat radiation and convection from the duct's surface.From: http://www.energysavers.gov/your_hom.../mytopic=12520
Hopefully, all the supply ducts are insulated in the garage, as well.
"If the furnace, is there any way I can seal it up (tape all the joints, etc) so it won't draw air from the garage anymore? " --- Yes, special ducting tape
Be safe, Gary
Clothes taking longer to dry?
Clean the dryer screen in HOT water if using fabric softener sheets.
They leave a residue that impedes air-flow, costing you money.
Clean the ducting in the last six months? 17,000 dryer fires annually!