Do car rental companies allow rentals in NJ and travel to Canada?

As you dont want to risk not being correred, ask the company and there may be an additional charge.

How the hell will the car rental company know you went to Canada?

yes of course, you just need to tell them that's where you plan to go and you will get a different rate for the car usage. Sometimes they give you a mileage limit, but if they know you are traveling a far distance then you get a different rate for that type of rental. Just be honest with them cause they will charge you per mile. If they know you will drive a far distance you get a different price range per mile.