You will collect your luggage at JFK after you clear immkigration but before you clear customs. Ask Turkish Airlines if your luggage will be checked through to DC and if they will issue the Delta DC flight boarding pass. If yes, take your bags to the Delta connecting flights counter after you exit customs and proceed to Delta terminal 3 via Airtrain and proceed through security to your departure gate. If no boarding pass for DC and/or luggage not checked all the way through you'll need to check in at Delta terminal 3.
You will collect your