For sludged engines, Widman (see Selection of the Right Motor Oil for the Corvair and other Engines) recommends the use of a 10W-30 Heavy Duty Engine Oil (HDEO) followed by 15W-40 HDEO because HDEOs have strong detergent/dispersant additive packages already built-in.  (See Widman's Bottom Line Recommendations: 10, 11, 12).  Keep an eye on the oil and, when it looks like it's thickening up, change it.  Detergents are polar molecules and work by displacing deposits from the surface of engine. Once removed from the engine's surface, sludge is kept from agglomerating by dispersants.  The net effect is that any sludge cleaned from the engine will remain suspended in the oil, without any danger of clogging the oil pickup screen.  For more severe cleaning, it is best to use a slow-acting cleaner (like Auto-Rx) rather than solvent-based fast engine flushes.

Widman's Bottom Line Recommendation #10 is:

Forget the myth that you can’t put high detergent oils in older engines or engines that have been using poor quality oil. I do it every day! 50% of this market is API SF or lower, frequently without thermostats. They are full of sludge. Some drain plugs come out looking like a cork, with an inch or so of thick sludge on the end. No matter what the engine, I put in a 10W-30 high detergent CI-4 oil and instruct the customer to come back when it thickens up, or the following week if he doesn’t want to check it himself. Once it no longer thickens up quickly we move on to 15W-40 and add a 1200 mile engine cleaner. At the end of that cycle we move to whatever oil the engine should have.

If you've just removed the valve cover(s) or oil pan and discovered sludge, you can use mineral spirits to wash the sludge off those parts.  Don't try to remove sludge inside the engine as hard deposits can be dislodged, which can later clog your oil pickup screen.  Don't be concerned with trying to remove insoluble varnish deposits as these are harmless and can eventually be removed by the detergents in your oil.

Widman recommends the use of pre-CJ-4 Heavy Duty Engine Oils in older engines (see Bottom Line Recommendations: 6, 7, 37).  That is, oils that are rated for both gasoline and diesel engines and that the diesel performance level is CI-4+, CI-4, or CH-4.  The gasoline performance level listed for these oils will typically be SM, SL, or SH. The upper part of the API donut would typically show a combined performance level like API Service CJ-4/SM or API Service CI-4/SL.  Since CJ-4 oils are much more common now than the earlier CI-4 and CH-4 performance levels and since these HDEOs are far superior to the old engine oils meeting the obsolete performance levels (ML, MM, MS, SA, SB, SC, SD, SE, SF, etc), we also recommend its use in any flat-tappet engine newer than 1930.