The oil port cap is plastic, so the flap holding it often breaks, but the cap will pop back in there and stay most times. The hub should get light oil through that port. Whenever I adjusted my cable, I always took the little chain out and put some light oil down in the opening, just for good measure.
Once you've gone through and set up your shift cable, it will seem easy. On the Sturmey Archer, in 3rd, high gear, the cable should have just a tiny bit of slack. Then you adjust if need be to get 2nd, and first gear. On the older SA's, there's a neutral position between 2nd and 3rd gear, where the pedals will spin free. If it's out of adjustment, you may find it the hard way, hopefully not while standing on the pedals.
Shimano 3 speeds, older ones, had a mark you adjusted the cable to, they didn't use a chain, they had a inner rod and mechanism with alignment marks on to get it just right.