How do you remove wax from linoleum floors...?
You need a liquid floor cleaner that contains ammonia. Ammonia is the secret ingredient that breaks down floor wax, as it goes after the cross-linked chemical bonds. You may need to use a high concentration of the cleaner, perhaps even use it straight, and allow it to soak in place for a few minutes to allow it to break down the wax. Then simply mop the floor to pick up the residue. A rotory floor scrubber (the type the professionals use) using either a mild abrasive pad or a polishing pad, will make the whole job faster. (don't use too abrasive of a pad, or it will damage the floor). Caution: avoid the temptation to use straight ammonia, as the vapors are too strong and could kill you! Just find a good quality floor cleaner that specifically states that it contains ammonia. Your local home center sells professional strength floor cleaners that will do the job.
Armstrong makes a stripper. I think they're pretty strong if you're going for natural. My son has asthma so I try to stay away from the chemicals too. Have you ever tried Borax? It's in the laundry aisle with stain removers. It's a natural powdered abrasive. Mix it into a paste with a little water and scrub with a pot scrubber. You can use it for a multitude of other cleaning tasks too. It's in a greenish box.
Try vinegar or white spirit on a small patch first
**** and Span will remove the wax.