Some US auto lenders will allow you to "transfer" the lien to Canada. I imagine the bigger finance companies with wings in both countries are the most likely to allow you to do this. I once heard that Ford Motor credit will allow this, but I can't guarantee they still do. As long as the lien can legally be registered in Canada, I imagine you won't have a problem registering the vehicle in any Canadian province. You are supposed to fax the vehicle title to US Customs 72 hours before you cross the border with the car when you are exporting it and one of the things they will check is to see that there are no liens. So you if you find a lender willing to let you transfer the lien to Canada, then I would suggest checking with US customs also to see what documentation they need to ensure that the car can be exported.
As far as how long can you drive the car in Canada with US plates after you move it depends on the province. Manitoba gives you 3 months after you move to register the car there. A US plated vehicle being regularly in Canada, particularly if it is not from a border state, will stick out more than a Canadian one driven in the US, so beware.