The Newark Branch didn't run all the way to Waldwick. The passenger timetables in the Official Guide show Newark Branch passenger trains running to Waldwick, but from Paterson (XW Tower) to Waldwick they were on the New York Division Main Line. In "modern" times (including the era 1945-1955) the Newark Branch left the Greenwood Lake Branch just west of DB Bridge over the Hackensack River at Snake Hill, and joined the Erie Main at XW. It crossed the Passaic River on NX Bridge, a bascule bridge still standing open.
The motive power on way freights in steam days would have usually been H-class 2-8-0's and (probably interchangeably) C-class 0-8-0's. In 1968, and probably much earlier, the Newark Branch job had an EMD switcher (SW-9, etc. or whatever was first out that morning at Croxton Enginehouse.) I remember one time in 1969 that was the power they had when the locals piled a baricade of debris on the track. When the train stopped the crew members were assualted and badly injured.