It's not clear to me what problem you are trying to solve. Are you trying to find when these folks died and where they were buried? And then to find their obits? Or, are you looking for baptism records for the children? Or, maybe you want all of these things.
Assuming the answer is "all of these things," I'd suggest working backwards. If the children died after the 1930s, you should be able to find one or more of them in the Social Security Death Index. With that information you can obtain a copy of their death certificate, which will give you the date and place of their death, as well as the date and place of their birth. I'm not sure about NJ death certificates, but it may say where they are buried. With a date of death in hand you can look for an obit, which will hopefully tell you where they are buried (if you don't already know from the DC) and give you more information about the family.
Getting back to your original question regarding newspapers, the big papers in the area today are the Star-Ledger and the
Courier News. Try calling or e-mailing the reference desk at the
Somerset Co Library in
Bridgewater. They will be able to tell you if those were the big papers in the 1930s. I think they have some of them on microfilm, but I'm not sure which ones. I'm fairly certain they can tell you what other facilities have copies.
As for which churches Germans attended, I guess a "modern"
German could attend about any of them. The early Germans were generally Lutheran or Reformed, both of which are still big denominations in the area.
One additional suggestion is to contact the Alexander Library at
Rutgers. The NJ Genealogical Society keeps their collection there, and there's an alphabetical card file of individuals buried in NJ cemeteries. It does NOT include all cemeteries, and I don't think it has been updated since it was created (which was probably in the 1930s or so). My NJ research has been with colonial families, and the card file was very useful. Anyway, you may get lucky and find one or more entries.
Good luck.