Set the new furniture inside a garage or other covered area for a few days to allow it to release any "off-gassing."
Raise the windows and open doors in your home if you don't have a garage or other area to temporarily air out the furniture. Run ceiling or oscillating fans to help expedite the removal of the odor.
Fill small bowls with baking soda and set them near the furniture with the varnish smell. This is an old-fashioned, yet effective remedy to remove offensive odors from refrigerators and other areas. The baking soda absorbs the odor and neutralizes the air. Leave the bowls out for two or three days for the best results.
Set bowls of white distilled vinegar in the room near the new furniture. Vinegar absorbs the foul odor and leaves the room smelling fresh. Leave the bowls out overnight or longer to give it time to rid the room of the smell. The vinegar smell evaporates within a half hour of removing the bowls.
Place two or three containers of activated charcoal in the area around the new furniture. It neutralizes the smell by absorbing odors in the air. Leave the containers in the room overnight or longer to take care of the odor.