These balls are about 40 yrs old and have been dropped on the tiles floor quite a bit and have marks from the tile on them

MAYBE CONSIDER SANDING AND RECOVERING l THINK ITS A GLAZE ON THE OLDER BALLS

tongue lashing

You can try warm water and soap. Do not use any abrasives they will ruin your pool balls. If that does not work they sell pool ball cleaners here http://poolndarts.com/81-Pool-Ball-Accessories/
If you do not want to order over the internet you can find them at most any billiard supply store.

l would buy new balls. Arimeth Pro balls are really good.

In a dishwasher.
Really, l am not kidding, it works really well.

You can not just wash them in a sink? What the hell.

if soap and water doesnt get it maybe looking at new ones is an idea. l mean 40 years is quite abit of use and all.

Considering their age and the fact that they have been being dropped on tile floors for 40 years, l would suggest buying a new set. If they have chips, cracks, or other imperfections the odds are they do not roll true. If buying a new set off balls is not an option use a glass cleaner. Other cleansers may leave a waxy residue that may leave marks on your felt.

Order Aramath ball cleaner or if really dirty ball restorer. Also l have been told turtle wax works really well.

Every answer l can think of still sounds wrong!