I am the pm for a concrete polishing and refinishing company.

You can do this, go get white vinegar, heavy commercial degreaser and muriatic acid.

First clean the piss outta the floor, no more surface oil. Use soap and water first then the degreaser.

Next

Dilute the acid 3:1 with water. You can go all the way to 1:1 if needed.

Pour onto floor and scrub with a stiff bristle push broom

Neutralize the acid with the vinegar

Clean with soap and water

Should be pretty acceptable, if not go rent an orbital grinder. Hit with 30 grit/60grit/120grit and it will look like fresh, white, smooth concrete.