CO's gem is EWR, they don't need JFK. CO is able to be much stronger out of EWR because they have feeder traffic from domestic flights and COex flights. UA, DL, and AA don't have a lot of feed into JFK, so they rely mainly on O&D traffic.
Northwest's nonstop JFK-NRT flight is operated under codeshare with Continental. As for NW from JFK, don't forget that they also operate short haul flights from JFW, with 1 DC-9 daily to MSP, and 2 DC-9's and 1 A-319 to DTW, plus one 747 to AMS, for a total of 6 NW flights from JFK a day.