I use Murphy's oil soap in a bucket of water. Using a sponge mop that really squeezes most of the water out of the mop I then scrub the floor. As I work around the room I immediately follow up each section cleaned by drying it with a sh-mop from Lowe's that has a towel like cover. That drying shines up the floor and looks fantastic.
You might have a buildup of wax or other substance that perhaps was not removed adequately when the floors were cleaned. If this is the case then you would need to find a good quality stripper which would pull-up the wax or other substance so that the woods finish would look more normal. It could be also that the wood itself has lost it's luster do to heavy use or similar issues and they need to be stripped and buffed to bring back the shine. The mops are probably also an issue as they do not really scrub the floor and you most likely are in need of a hard-floor cleaner. I purchased a Hoover dual surface cleaner, hard-floor and carpet, a couple of years ago. It was not cheap but I got it on sale as the regular price was over $500. I have tile floors and could never get certain areas clean. This machine on it's first use with the proper cleaners did what I hadn't been able to in several years with mops, brushes and anything else I could find. Check them out as the newer one's are superior and also much easier to use as they are very similar to a vacuum.