ive got a shimano 3sc hub as wel, and as you know, there is no oil port in it. i was once told that shimano used a special thin grease to lube the internal parts, but of their own making. i definatly would not use any old grease inside a 3speed hub as they may gunk up any pawns or springs. if i couldnt find the special grease used for these things, id maybe do the outter wheel bearings with very light grease and a light machinists oil or atf for the hub itself. its twin wo/coaster brake, the 333 hud uses oil so id lean that way. obviously wo/ an oil port, its meant to be lubed only when rebuilt. now if its still intact and needsto be lubed, id pull the shifting rod out the axle hole and drip a little light oil down the hole in the axle into the hub. good luck.
Thanks for the reply. Mine really has a port, it almost looks like a grease nipple. I did not mess with it and I like your idea about the shifter rod hole. Though it seems fine, it is a 70s model and likely never had service in it's life. I will give it a little dose of oil.
Mine doesn't have a oil port either. I took it to the lbs for servicing, hoping to get more life out if it even though it works fine. They suggested it be left alone unless it has a problem.
if it has a port, a few drops of oil every month is what is recommended. if not, and your hab starts to run dry or weird, a few drops down the axle hole will help. just, no grease.