My landlord will soon replace inside doors with new ones that he'll have covered with some varnish. I told him I'm concerned about VOC (I remembered using a high VOC paint on inside door in some previous home and it spoiled our lives for 3 days). He reassured me that the varnish is quick drying, but is the problem about drying speed? Can a paint/varnish be dry yet still produce VOCs?
In general, clear coatings today have been reformulated to product much lower levels of VOCs (volatile organic compounds) then even three years ago. Not knowing what product he plans on using, varnish, urethane, lacquer and the age of the product makes it difficult to guess how long the finish is going to take to gas off. Most modern products gas off in about 24 to 48 hours. Although you may still smell a slight "new paint" smell, most of the irritating fumes are pretty much gone after a day or two. Just ask your landlord to give the doors a few days to cure, not dry, before installing them.