If the finish is sound and a film finish, I have no problem using water-based cleaners. Normally, I would use Dawn and water.

If this frightens you, you can use an emulsion-based furniture polish (which by its nature is 80% or more water). Guardsman Furniture Polish and Oz are two name brands.

Mineral spirits or naphtha will remove petroleum based products, but little else. If if removes other stuff, it will do it weakly and mostly due to abrasion.

Mineral spirits removes dust and dirt as well as any water based cleaner will....without the danger of water entering a compromised or thin finish or clouding a shellac finish.
Mineral spirits will also remove old wax, grease, like food grease, tobacco and smoke residue...but won't remove sugar based soil...like pop, milk, frosting etc.
Linda C

Mineral spirits is also great for the general grunge that is made up of dirt/dust mixed with skin oils, like you get on wood banisters, wood chair arms, etc. I've had much success with it: my folks learned this in a furniture refinishing class. If the furniture is just deeply dusty without grunge, though, it may not be necessary. I've brought furniture from the parental attic that was just deeply dusty in the carvings. For that I used a vaccuum cleaner attachment in the left hand and a clean white china bristle brush (stiff bristles) in the right, to dig out the dust while the vaccum nozzle followed behind. The vacuum attachment with bristles was too soft to be much good.

LOL! linnea! Please define "grunge"...general and otherwise!
Linda C

Thank you everybody. Whew!!! I got through getting all the furniture back in place after three months of the insurance company putting down new wood floors after the flood. The cleaning people didn't seem too with it. But I learned a lot from your help and ideas. I think I will try a little mineral spirits on some gunk. I remember my Dad using it on lots of things. I believe they even cleaned spots on clothing, i.e. wool coats, etc. Thanks again for your help.