Go to the hardware store and purchase a set of small screw extractors (less than $10). Drill the correct size hole, place the extractor in and turn to the left. There are special tools for the one-way screws, but they are not readily available.

so I finally got to buy the screw extractors
(Black & Decker set of 5 with NO instructions enclosed). Package says
for removal of screws with broken/damaged heads. But my screws are one-way and still have heads. Reply said to drill proper size hole so I tried to drill thru the screw head. I broke 2 small bits (for steel) then tried larger ones but no good. The tops of the screws are still there. HELP!

The bits broke for one of two reasons:
1. They were dull so that you tried to press harder and snapped them.
2. The screws are of high alloy steel and mar require a carbide tip to drill through.

Your only other possibilities may be to grind the heads off with a high speed grinder or to begin chiseling them off. You may be able to use a Sawzall type saw to saw right through the hinge and screw. These will allow the shank of the screws to remain in the door, but the hinges will come off and you can make a small adjustment in the new hinges for new screw locations.

I know the extractors are for broken screws and bolts, but the principle is the same.

I know from experience that all of the methods I have mentioned work to accomplish the task. At times it just takes more effort to do the most simple things.

u talk about hinges, but there aren't any. This is a Segal lock, keyed on both sides, about the size of your palm, that attaches to door with 4 screws, and drops 2 bolts into a hole thing attached to door frame. The screw heads are sunken/flush into the holes and unaccessable. I even tried to get between the back of lock and door to try to saw screws - with no luck. I hate to sound stupid (I'm usually quite successful with my tool box) but I need more help here. Thanks again!

No offense, but its time to call in a locksmith. I think you've reached the threshold where aggravation costs more than the locksmith.

It sounds like your screw heads are case
hardened, because they broke the drills.
Grinding will certainly do the job, but if
the heads are close to flush, not too deeply
recessed, there's one last hand-tool approach
to try:

Get a center punch and a light hammer. I
wish I could draw you a picture, but....
Pick a point in the cam-out part of the slot
in the head that's near the edge, but still
has some room for the punch to dig in. You're going to be tapping gently on the
punch, but not perpendicular to the door.
You need to lean it over so that the tapping
will tend to move the screw counter clockwise. For instance, if your punch point
is at the twelve o'clock position, you'd lean
it to the right.

Tap a little, then pick another point on the
opposite side of the screw head, and tap
there. Go back and forth between the two,
and see if you can get it to move. Silikroil
or WD-40 may help.

This is just one last thing to try before
renting a grinder or calling the locksmith.

-- J.S.