I cannot speak specifically to your routing, but in the past I have booked connecting *A flights (UA JFK - LHR connecting to SK LHR - OSL) and the JFK check-in staff was only able to issue me JFK - LHR. The only instances where I have been able to be checked all the way through were codeshares (not sure if this is always practice or just my experience).

In any case, I would guess you will have to check-in in SIN for your OS flight. I would try and find out though if you can check in at the gate for your OS flight (not sure about the SIN airport layout).