Hi John,
I would go the other way. If you have the time, and are handy, and want to save on money I would rent the belt sander from home depot, the one that uses the round sand paper ( not the flat square one). Makesure you rent the edger as well. you will also need a little orbital sander for the corner. By alot of sand paper because the paint will gum it up.
My husband have salvaged some pretty terrible wood floors. Its a lot of work sanding through paint, I think you will find that paying someone would be extremely costly. You will probably use up all the savings and in the end you might as well have installed new prefinished wood.
About 10 years ago, I sanded a 900 square foot apartment. We removed the raspberry colored carpeting to find nice wood floors that had been painted with a dark brown thick enamel paint. I spent the whole weekend sanding - but the end result was great! They are beautiful. I haven't had to do anything but shine them in all these years. As far as the plywood floor- you have nothing to lose, pull it up and check. If the floor has dark stains from something like water damage - use a dark stain and it should hide it nicely.