I can’t answer with complete accuracy, but I can hazard a few guesses. IAATC (I am a train conductor) but obviously not with NJT.
The slips of paper I’m familiar with are the same dimensions as the ones you describe, though I’ve only ever seen the backs of them used - on long-distance trains. The conductor or one of the assistant conductors comes by, takes the ticket, and then writes the station code of your destination in black magic marker on the (blank) back side of the slip, then sticks it under the metal tab above your seat that displays the seat number. So, if you boarded in Dallas and were headed for Marshall, your slip would say “MHL.”
The slips come in different colors, with white, light red, and light blue being the ones I see most commonly. Whether the colors are part of the ‘code’ or not likely depends on the policies of NJT or perhaps that particular train crew.
On the ones you describe, it sounds to me like the E/W is meant to signify eastbound or westbound - the trains probably make several trips a day each way with the same crew. I should note that it’s traditional for passenger trains to be coded eastbound or westbound regardless of their geographic direction. Amtrak’s Texas Eagle, for instance, runs from Chicago to San Antonio. When the train is literally going south, it’s classified as a westbound train, and vice versa. Some of the commute trains on the old Southern Pacific were labeled eastbound when they actually traveled in a western direction. Just a quirk.
The numbers, if I had to hazard a guess, would be stations. Rather than print a set of slips specific to each train (which would have station names pre-printed) the railroad likely just gets all of the slips with these numbers and each train crew knows that stop 2 is “Doperville” or what have you. That would explain why there’s no 1 - it’s impossible for your destination to be the initial terminal.
As to why they sometimes tear the slip or punch holes in it, that too would be up to either the railroad policy or the particular train crew. Again, if I had to guess, I’d say that the Lead Conductor just puts the slip up, while the assistant conductor punches one hole in a certain spot, and so on. I’d imagine on a commuter train there would be several assistant conductors, but I don’t know that for sure. At any rate, that would let everyone know instantly who held that person’s ticket stub - each conductor has a pouch. That way if there’s some sort of problem, the conductor can see that a hole is punched, and he knows to call Assistant Conductor One on the radio to bring his pouch.
Those are just educated guesses, as I said. Unless we have a NJT Doper, I suppose the only way you’ll know for sure is to ask next time you’re on the train. The answer will probably be at least as mundane as my suggestions.