So you currently own this US-origin car in the USA and have owned it prior to and through the dieselgate scandal, and you are now moving to Canada and wish to take the car with you? Is that the situation, or something like that?
You will have to go through the RIV process.
www.riv.ca
Part of it involves obtaining a letter from the vehicle manufacturer declaring that the vehicle has no outstanding recalls. This will be your biggest obstacle. Try to get that document before you proceed any further. Transport Canada will absolutely not allow the vehicle to be registered in Canada without that document. I don't know about VW, but lots of vehicle manufacturers flat-out refuse to provide that document, thus leaving you stuck and unable to proceed. This is one of the other ways that the manufacturers discourage people from doing this.
When I did this with a motorcycle a couple of decades ago, I knew the chap who I was buying the bike from and he was good friends with someone at the dealer, and they wrote something up on the manufacturer's letterhead. (I still have that bike)
None of this addresses the warranty situation. VW Canada's position will almost certainly be "not ours - not our problem".