I live in a area with many private landing stips within a 5 mile radius of my home.  DJI's map and Hover just show the airport while Airmap and B4UFly show everything.
Do I need to call each place(4) to report flying or just the local municipal airport?  

If it shows up in B4UFLY then it's very likely that the FAA considers it an airport (or heliport) for notification purposes.

Just to CYA I'd attempt to call the strip. My guess is that they don't have a phone number or a number that works. At least if you get in trouble you can say that you attempted contact.