Your oil rings are gum-stuck in their grooves..
I'm not usually a fan of many "mechanic in a bottle" treatments, but Seafoam is an exception. For cleaning out a really varnished or gummed up engine, it does pretty good. Pick up a bottle or two.
First, you want to decarbonize the chambers and intake valves. So you'll use about half a bottle by slowly pouring it into the carb with the (warmed up) engine running. A little in one primary barrel, then a little in the other. You'll need to crack the throttle by hand to keep the engine running as it will want to stall. I usually use about 1/4 throttle and give each barrel one little hit and then one big hit letting the engine stall out after the last hit. Let engine sit for 10-15 minutes. Pour the rest of the first bottle in the gas tank. Pour the second whole bottle in the crankcase (you're gonna change oil in 100 miles). When you start the engine there will be a cloud of smoke and little bits of carbon and sludge will shoot out the tailpipe (so you either do or do not want to do this upwind of your neighbors dinner party).
Don't run the engine too hard with the Seafoam in the crankcase, in fact it works better with stop and go and short trips. Drain after 100 miles, and replace filter. Fill with Wal Mart Synthetic 10w30 and take the car for an extended highway drive. Preferably a route with some hills. You want to really get everything hot and moving. If the engine was a total sludge monster, you do stand some risk of having all the sludge loosen up at once and clog the oil pump pickup. It was going to do this sooner or later anyhow, so just turn towards Pennsylvania and shake your fist at the Quakers and their waxy oils.
An alternate way to free rings, and I do this to engines that have sat dormant a long time would be to pull the plugs and give each cylinder a good shot of PB, Kroil or Liquid Wrench a day or so before I try to start it.