How Do I Repair An Outdoor Faucet That Is Badly Stripped? The Water Won't Shut Off, Even Though I Shut Off Main Water Supply Into Our House Located In The Laundry Room.

Shut off the water at the water meter.   At that location, you're assured that cuts off the whole house and the yard.  Then find the lowest point and drain the house plumbing and replace the whole valve.  Replacement valves are pretty cheap so it's usually not worth trying to fix the valve seat or gaskets.

It sounds to me that the main valve feeding the home is not seating properly..if that is the case you should call the water dept. Or a licensed plumber to fix the valve....think about it ...if you have a MAJOR LEAK  how will you shut off water to the home ...a expensive insurance claim or replace the valve!! It's a NO BRAINER!!!