I've never liked the smell of petroleum based solvents. When I can avoid them I do. I select finishes that are lower odor because it isn't always possible to do finishing in my garage so I often need to finish in my house where odor is a problem for my wife and me. Fortunately, there are a few options to solvent based varnishes.
Tried and True is a brand of woodworking finishes that is free of petroleum solvents. There is almost no odor at all. It comes in oil, oil/wax blend and varnish oil. I believe they are all based on linseed oil but do not contain metallic driers or petroleum solvents like other boiled linseed oil products. They perform some process on the oil that allows it to dry without the other additives.
Shellac is another finish that has lower odor. Shellac is cut with alcohol. The odor of pure alcohol is very low compared with most varnishes. While denatured alcohol is poisonous, I feel much safer using shellac for a finish because the alcohol evaporates so quickly.