Oasis lounge (T4) and AF T1 lounge are both very nice. But I'm not sure you can use any of he skyteam lounge in your case. If they all were in the same terminal, OK but as it's not the case, I don't think it's possible. You need to use a lounge in your actual terminal of departure. If you go to AF lounge in T1, first I'm not sure the TSA will let you go through security (with a BP for a flight leaving from another terminal) and if you go through, how do you go to T4 after ? Term 1 at JFK is a pure international terminal, so there is no domestic exit AFAIK.
Oasis lounge in T4 is landside, so easier to handle in your case (if you want to give it a try )