If they died overseas and were returned to the USA after the war there are several methods to determine the date and possibly the cause, as well as other information regarding unit etc.
First:You must determine their service number.(ASN) If you can tell me what town in NJ they lived in, I can get this from National Archives in about ten minutes.
Second: What branch of service were they in?Army/Army Air Forces, Navy or Marines.
Third: Where were they buried in NJ?By going to (or calling) the cemetery you will likely find the marker--either marble or Bronze--that would list their unit and date of death.
Fourth: When you have the service number you can send a written request to acquire their IDPFs (Individual Deceased Personnel File) File 293.This will have a great deal of information that will be helpful to you.Keep in mind that theIDPF may be graphic in its contents, especially if the casualty was a victim of a plane crash.These usually contain skeletal diagrams.
Please feel free to drop me an emial to the address behind my name at the address bar on this posting and I will get you started.