Chain dies under light load, engine running ok

Not right ideal settings!

It probably is not getting enough fuel. Check the filter in the tank. If it has been sitting with stale gass this filter plugs up.
Try running the engine with some choke. If this helps, try adjusting the carburetor high speed screw.

Quit doing what you are doing before you cut yourself. The cut could kill or cost $10,000 just to live with an ugly scar. You chain is not staying adjusted correctly.
My Homelite does NOT do this. But my neighbors Poulan did. It thrashed the chain against the spike and threw it completely off. The adjustor didn't work right and an attempt to bolt it tight also failed. So I ordered the spike and the whole cover/brake handle/chain adjustor kit for it. Should get here from Sears in a week for under $40 USD.
URL: https://www.searspartsdirect.com/partsdirect/
Mod: PP4620AVX.
Parts items
(45) Spike 530014381 and
(70) Kit ezt c/br 545081874

I don't know what suppliers you have in your area but where I live tractor supply, orechlins,and true value all have good selections of chains and knowledgeable sales staff. Most have a selection booklet that lists proper chain selections fo bar length, manufactures, chain type [ low kickback, fast cut, etc.]
You will need model number, manufactures name, chain length, type of chain you want. I would use the low kickback chain in almost all types of wood. About the only type of wood that I would use a more aggressive chain on is soft high moisture content woods like cottonwood or certain elms and pines. I hope this helps you. Thanks

Organ makes a replacement combo bar/chain for the j3816. Part # is 105700. You should be able to find it in most stores like Lowes or Home Depot. You could also go on line to wwwOrganchain.com. Hope this helps.

It is normal for a chain to loosen under usage, especially if the chain is dull or mis-sharpened so that the chain must be overly forced into the cut or there is insufficient oil being fed to the chain from the auto-oiler. Remove the bar and chain--start the engine and look for oil oozing out of the side port in the engine where the bar fits to. If there are thin metal plates on either side of the bar, make sure that the one with a long slot fits to the engine side. This slot allows oil to enter the bar oiling holes no matter where the bar is adjusted. Be sure to clean the two small oil passages in the drive end of the bar that run from the large holes out to the chain groove on either edge. Clean the chain groove as well as the bar and engine side. Reassemble the bar and chain making sure the adjustment 'tang' drops into one of the large bar holes. Install the cover, but leave the mounting nuts/bolts finger tight. Turn the chain adjustment screw CW until the chain just pulls up to the lower bar edge, then tighten the cover mounts. Make sure the chain can be turned by hand and is fully up to the bar with light tension. Chain filing is fairly exacting and must be consistent from tooth to tooth. If a tooth edge cuts your finger, it is considered to be sharp. (not a suggested test by the way) Look for no light reflecting from the filed edge as a good test. Once everything is ready, start the engine and run the bar tip near some cardboard--a few moments running should produce a thin line of oil. If it seems slow to cut, check the chain's sharpness. Don't worry about adjusting the chain to some mark as the chain will grow length with use. It is not necessary to remove the bar and chain when adjustment is required, just loosen the bar mounting fasteners to finger tight. Hope this helps!

Before adjusting anything, check the fuel filter, air filter, and muffler for plugging. Check the condition of the fuel lines for decay or other damage. Tighten all carburetor fasteners. Make sure you have fresh fuel mix in the tank. Does the primer bulb pull fresh fuel into itself when pumped? Turn both jet screws CW to stops (lightly), then back out CCW 1-1/2 turns each. This is a basic setting and should allow the engine to start and run. Start the engine and allow it to warm up, then pull the throttle full on. Adjust H needle CW until the engine starts to speed up, but still 4-stroking. Proper final adjustment is when the engine 4-strokes unloaded, but immediately 2-strokes when cutting. Release the throttle and adjust L needle CW for fairly good idle, but still allows the engine to 'follow the throttle'. Adjust idle speed screw so that the chain stops turning, but the engine will continue to run. Hope this helps!

The make, model, and occationally the serial number help us solve your problem.

Does the engine quit running? (Carburator needs adjustment)
Or does it continue running and chain stops? (need clutch refaced or replaced.) (to aggressive a chain for the size of the engine)

I think you replaced parts unnecessarily. Maybe quicker and cheaper to visit your friendly neighborhood chainsaw shop. A good one can repair it even if they do not sell your brand.
HTH
Lou

Could be the internals of the clutch have been heavily oiled--wash out with carburetor cleaner from an auto parts store. The internals of the clutch expand to the internal rim of the clutch housing when things rev up. Oil blocks the necessary friction needed between those parts. Make sure the chain sprocket is attached firmly to the clutch housing.

Check the muffler screens first. Then the spark plug. If not the case, then adjust the High setting on your carb. Prolly starving for fuel under engine load. If it is still a problem, Pull the carb and clean it.