As the question states, I am looking to remove a thoroughly stripped screw (the head is stripped) from a hard disk drive. My main issue is that I have no power tools available to remove the screw. How might I be able to remove the screw without drilling it out?
You can use a good knife or other very sharp and very hard tool and make small parallel scratches on the screw (whatever is left of it), alternatively one deeper scratch in the middle. Then use the hack of abby and a flat tool. I found it most useful to use the inbus (hexagonal screw) bit of my tools to be perfect for this. Depending on the situation you have at hand a rounded tool may be of more use.
You need to apply a lot of downward force on the tool to do this.
That way you will press the rubber band into the small scratches and when you turn the tool it will start twitching slightly. This takes some time to produce results but works. You can monitor the progress if you make the scratches parallel to something nearby.
This assumes the screw will turn at all, so you might need to lubricate it before doing this. If its rusted in or otherwise totally unturnable, you might have lost.
The correct screwdriver should be used, first of all. Often times the correct screwdriver will grab the screw when it appears stripped. A sharp screwdriver should also be used, not having rounded edges. A correct screwdriver generally involves using a phillips instead of a reed-and-prince which has a sharper point, and a #2 screwdriver instead of a #1. Very seldom is a #1 screw found on a computer. Screws may be small, but are still #2. If a #2 even begins to fit the screw head, it is a #2 screw. The same cannot be said for #1.
In the Air Force I learned the correct way to remove a screw. Many seemingly stripped screws can be removed this way. As mentioned, use the correct screwdriver. Second, apply downward force. Third, bump the screwdriver and do not twist. Usually a slight grab can be felt, but the screwdriver rotates off of it. That slight grab can be exploited. By using a sharp screwdriver and bumping it, going back and fourth, that slight grab will wear into a shoulder large enough to wind the screw with. It takes a certain feel to do this which is not hard to acquire.
I want to follow up by saying how to prevent stripping a screw. Go ahead and twist most of the way in. When it gets to the last and starts becoming tight, stop twisting and start bumping. Use small bumps and never large moves.
How about trying to epoxy or super glue a tool to the screw? Or glue something to what's left of the screw so that you can grip it with pliers or a wrench?
This can be precise work, so you might want to mask off areas you don't want to get adhesive on. You could use what ever you are going to glue to the screw as a punch through the masking tape to create the mask.
there is a tool called an easy-out that you can stick into the chewed-up screwdriver hole of a phillips-type screw head and, grasping the easy-out with a pair of pliers, unscrew the stuck screw. It may be difficult to find one small enough for your hard drive, but well-equipped hardware stores have them in a variety of sizes.
Don't forget that you can cut a slot into the head of any screw with a worn socket. A small grinder such as a Dremel Tool, or a fine-tooth hacksaw if you can get at the head of the screw or don't mind defacing the surround especially if it's a washer or bezel that can be replaced.
Also, there are various other shaped driver blades that could fit a worn/stripped Phillips, posi-driver, or screw-lox screw head socket such as a square-head Robertson driver.