Look in the phone book for various cleaning companies. Some of the carpet cleaners do floors too. There are various products they can use on wood floors. BONA makes a cleaning machine that might work for you that some of these guys use now.

Sometimes the black is embedded dirt in the finish, especially in heavy traffic areas. May be necessary to remove the finish with paint remover and a brush, then refinish floor.

I have not done this myself, however, my search for same problem tells me this is the last straw other than replacing the wood floor.

I have oak floors on my main floor. I noticed black streaks near my potted plants. Appears the pots overflowed when watering and the water damaged the wood, causing these black areas. They won't wash off. Believe me I've tried. I say live with them, consider them part of the floor's character. Then you could always 1. refinish the floors or 2. cover with nice are rugs. I've been in some fancy restaurants in my time and I noticed the ones with wood floors always show plenty of wear and damage. Consider it part of your home's charm. as long as it's not washable, it's not really "dirty".