House was built in 1944. No insulation in the in between joist. Celing-drywall/air/plywood-on the top covered with tar. Can I put insulation on the top of the plywood and what thickness/R-number.

The air space between the drywall and the plywood is the place for insulation. You also need a vapor barrierimmmediately above the drywall and also some soffit vents. However, this would require dropping the drywall. I'd call some insulation contractots in your area to see if any of them can bid a blown in insulation which would only need small holes every few feet.

Thank you for your advise. So if they blow in the insulation, how and where the vapor barrier would go?

If you go with blown in they can not install a barrier. You could go with a slightly less effective paintable one. PRP1, Perma-Prep Interior Latex Vapor Barrier Primer/Sealer, Not Avail

Since the celling is in pretty bad shape, I'll tear it down and install the insulation in between the joists. What kind and how should I install barrier?
Thanks.

Measure how deep your rafter cavity is and buy rolls or batts the same thickness, I'd get craft paper covered. After stapling in place cover the entire ceiling with one big piece of plastic, like 6 mil visqueen.