A common problem is having to remove a screw with a stripped head. Either the person installing it stripped the head as they installed it or the head is still intact but it is so frozen by rust or other issues it won’t budge.
This is common in door hinge screws and in this video it was from rust.
The trick is to get a starter hole in the head of the screw, be sure to keep it in the center of the screw. Sometimes I drill a smaller hole partway in, about 1/8”, which allows me to angle the drill in order to drive it to the center (when and if) I get off.
Then I use a drill a little larger than the shaft of the screw. As you drill you’ll see the screw head spin off, perfect.
Now you can remove the object retained by the stripped screw and see a little bit of the remaining shaft. A newer pair of vice grips, because the old ‘grandpa pair’ has worn jaws and won’t grab right to the bitter end.
Go easy with the pliers, sometimes in both directions just a little bit, until you get enough movement to remove it.