DD,
I remodeled my garage this spring and I painted my floor with an epoxy finish. It also had some
oil, paint/woodstain and some kind of shelac stain in/on the concrete, about 12 years worth from previous owner. I used Behr concrete cleaner/degreaser with a hard bristle brush attached to a broom handle and alot of elbow grease! For the very hard shelac and stubborn grease, I used mineral spirits. Take your time and work the stains out before you paint your surface, they will bubble thru or not allow the material applied to adhere if not totally removed.
There are some pics of my garage in my gallery.
Hope this helps.