Painted double basin metal utility sink. Is this worth cleaning up?
Paint strippers good for oil paints are readily available.  One popular one is called "Aircraft remover".  It will go after alkyd enamels and lacquer paints quite effectively if used as directed. 

Don't assume the paint is "oil based" merely because it is not latex based.  There are some much more durable coatings out there, most of them 2-part like an epoxy. 

A great many such sinks are made of galvanized steel wrapping around concrete.  If they are heavily rusted, they may look black.