Your question is similar to one I hear often from my clients. Let me tackle it in two parts
1. Zip codes
The zip codes do not always represent different towns, they are sometimes merely for the mailing system. Towns often have several different mailing zip codes but they are part of the same township. Also different towns, can be in the same township.
As for the schools, the districts they draw for which students go where do not always follow the lines of the town. Sometimes, as you encountered, children from the same town go to different high schools. This usually is done in order to alleviate crowding in the schools, but also for other reasons. Some towns have multiple elementary schools so children attend different schools within the same town. It is less frequent but does occur that elementary school kids go to the schools of a different town. Also some towns do not have their own school system.
3. House value
School systems greatly affect house value, but in regards to redistricting there usually is a minimal effect on house values. The schools are usually of similar quality (but not always). Sometimes buyers shy away because they want their children going to a particular school. Difficult to give a general answer to this, best answered on a property by property basis.
I gave a general overview in answering your question. It would be much easier to answer your question about specific properties over the phone. Online you can try using NJ's DOE website, but it is not user friendly, instead rely on an agent.
Artyom and Natasha
The Rogov Team