If you can't find Sturmey Archer Oil, the next best thing is Phil's Tenacious Oil which you should be able to find in any bike shop. I'd believe they suggest oiling the hub with 3-5 drops of oil per week, something like that. Have you tried the chain tension adjustment? It's very simple but could take a few tries to get it right.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72