This is no mystery to me, but the stores now only carry pre-finished floors, and don't appreciate the beauty of a old waxed floors like we do. The best way to clean this floor, is of course never with water. You will need to use odorless mineral spirits. If you have little or no finish left on the floor you will not be harming it with this mild solvent. Use a white non abrasive scrub pad, while squirting the solvent on the floor. Before it dries wipe it up with lots of clean rags, until the rags are just wet with solvent, but not dirty. Let the solvent dry overnight, then apply a liquid paste wax this time.
There are two brands mentioned in the maintenance article in the Floored News section of this site. And a lot more info on just how to treat floors that have a finish you cannot identify. Yes, there is a finish on that floor, wax is only a top dressing for a sound finish, and someday you might have to remove the wax and repair parts of that finish, so please read the article. You will only need to clean and wax once a year, and just do touch ups and a monthly buffing with a natural fiber (corn broom bristles) pad on an electric buffer. And of course vacuuming often, and no outside shoes should be worn on this venerable old floor.
As always your Most humble servant, Joseph, the Wood Floor Doctor.
You may also find these articles helpful:
1. How To Clean And Maintain Wood Floors PART ONE
2. How To Clean And Maintain Wood Floors PART TWO
3. How to remove and clean various stains and odors from wood floors
4. Floor Types And Finishes
5. How To Take Care Of Your Health And Safety when Installing, Finishing, Repairing or Cleaning your wood floors