You can check your bags all the way through as long as its either all on Delta or there is a baggage agreement with the other airline. International baggage rules apply as long as when you check in you show an onward international ticket (DL or OAL)
Make sure if you have them link your records, still check your seats and flights periodically to make sure nothing changed. When they are linked, all it does is show a human that is looking at the reservation that you are traveling with someone else, there is no way to tell the computer system you are traveling together if you are on different reservations.