Can a Norfolk terrier be trained to stay in my yard without a fence and to walk off leash?

Terriers are instinctive vermin hunters and except in very controlled circumstances, cannot be trusted off leash or in an unfenced are at any time.  A rabbit or squirrel is enough to send them chasing, which may lead to being lost or hit by a car. 

A fenced yard (or dog run) is a must, unless you are committed to "potty" walks multiple times a day.  Tying a terrier out in the yard is not recommended, because it leaves him open to attacks by other dogs or theft.  Nor is an " invisible " fence recommended.  Many terriers will take the shock in their determination to hunt and don't return. 

An invisible fence also leaves them open to attacks and theft.  If you do not have a fenced yard your dog should always be on-leash when outside.