These things are caught in hard wood. I made the dumb mistake of not drilling pilot holes.
Rubber band trick failed Screw drill and removal bit failed JB welding a bolt worked for 2/5. Trying again, failed for the remaining three a third time.
Anything tougher to get these out? Any tricks to get more hold on the jb weld?
Locking pliers, which is the generic term for a class of product often called by the name of one registered trademark (Vise Grips® - no particular endorsement implied, but some of the cheaper knock-offs are quite useless. I believe Mole Grips® in the UK)
You need them clamped on hard enough that they actually bite into the screw head. With that presentation, you'll only get a fraction of a turn at a time. And depending on how hard they are stuck, you might break the screw (at which point you drill around the screw with a hollow bit and remove the wood plug and screw carcass together)
Vice-Grip pliers. If anything is sticking out always go Vice-Grip route.
Hot screw.
Get the screw hot enough that the wood it is in smokes. The metal will conduct the heat down into the wood. You could use a soldering iron or a torch or even a cigarette lighter.
Let the screw cool back down. The charred wood will be less enthusiastic about keeping it when you twist it out.
When the head is protruding as in your picture:
If those don't work or if the head isn't protruding try a screw extractor. Use the right size, read and follow the instructions.
As a last resort, cut it off at the base and move the piece being screwed or drill in to the wood at a slight angle next to the existing screw. In some circumstances, such as hanging something on a wall where the position can easily be moved slightly, this might be the first resort. Just cut the screw flush with the wall, move the piece up a little and start again, covering the broken screw with the piece.
Similar to the screwdriver slot - Grind two sides off the head to leave two parallel sides as wide as the shaft of the screw. Use a good spanner with a close fit, or the aforementioned vice-grips on the new flats.
You can use a strong drill bit to go down beside the thread and remove some of the wood. This is similar to the heat/charring suggestion elsewhere, but with less fire. Downside, leaves a raggy hole that needs patching/filling
And the last resort is to grind - cut the head clean off. Remove the pole/flange thing that was bolted on. Then use the grinder again to trim the stump of thread flush with the wood surface.
To make it look pretty, grind it below the surface, fill with bog/filler, then sand and paint. This assumes the screw is stainless, else rust may be an issue later.
Back in my military aircraft maintenance days, we would use these awesome tools we called a 'Johnson Bar'. Uses leverage to extract a stuck screw, bolt etc. Usually fom the last guy that monkeyed them down too hard. Might be a bit overkill for the average person and their issues but if you are dealing with this all the time, then perhaps it is a wise investment?
Check it out here: https://www.usatco.com/item/BRUTUS+SCREW+EXTRACT/Brutus-Screw-Extractor/
A pipe wrench is one possibility.
Drilling down into the bolt and using an “easy out” is another option.
Welding (arc or mig / tig) a nut onto the bolt is another, but protect the surface from spatter.
In the list of suggested ideas, one technique has been omitted, which works well with both wood and metal bound screws.
To use a diamond punch, the sharp edge is tapped into the fastener head as close to the periphery as possible. This creates maximum mechanical advantage. Taps on the point burrow deeper into the fastener head, and transfer increasing torque with a deeper pit that the punch rides in.
To make the punch, one can take a conventional round punch, grind it at an angle, say 45 degrees. Then grind down the sides, leaving an edge which goes diagonally across the face. Then grind opposite relief on the edge to strengthen the taper around it. It will look like an "A" offset to the side of the punch. Others describe the point as a steeple skewed to the side, so that a low rotational hit can be made.
When grinding, cool frequently so as to not modify the hardening of the punch. A very sharp "peak" or point helps dig into fasteners.
I have made several of these, as small as from a 1/8" punch up to a 1" punch, which is used on farm and construction equipment.
Impact from the hammer helps shatter rust structures. In wood it is not quite as effective, but it does overcome the static friction of compressed wood fibers.
What I've done in the past is to use a drill, locking the chuck directly onto the stripped screw or bolt. You need to make sure there's enough room for the chuck and drill to do this straight on, and make sure the chuck is tightened to the absolute max that you can. (I've tightened the chuck hard enough to deform screwheads/threads to make this work.) If you don't have this straight onto the bolt/screw, you can get some really nasty extra motions involved which can cause damage to you, the drill, or other items in the way of the drill.
FYI, you'll need to remove most of the JB Weld to make this work, but that'll mostly happen naturally as you crank down on the chuck. Just make sure to remove the chunks of JB weld from the chuck before you start extraction. You don't want any debris in there that could prevent you from getting the contact required for this to work.
If your drill spins on the bolt, but the bolt doesn't move, you don't have it on tight enough. This might even cause your chuck to slip off, which is a bit dangerous on it's own. You might have to use the edge shaping options some of the other Answers talk about. The difference between using this option and using a socket on the edge shapes is that this puts a lot of pressure to clamp onto the bolt that the socket just doesn't do. This ends up being a combination of using a locking plier and a socket. However, with the 3 jaws in the chuck, you'll get a way better grip than the locking plier. (BTW, a locking plier can all too easily slip off the bolt, even if you do shape the sides.)
As well as spinning on the bolt, you may end up breaking the screw/bolt. This is usually more of a concern with small screws, but it can happen, so it needs to be said.
Doing this can be a bit dangerous, so take it cautiously, but if you apply power slowly, it can work when all else fails. You need to make sure you have an absolutely firm and solid grip when doing this, as you are putting your force against the whole of everything the bolt/screw is stuck against. In your case, you can butt the drill handle/grip up against the pipe so it takes the force, instead of your wrist. With the pipe, unless you hold the drill solidly, you risk slamming your hand into pipe as well as wrenching your wrist badly. I've heard of people breaking their wrist using a drill normally, and this definitely has more force involved than most drilling applications.
I recommend using a corded drill, as they tend to have more torque available than a cordless*. However, if you have a pro series/brand &/or impact cordless and a tiny cheap corded drill, your cordless might end up having more power.
Note: This requires a variable speed and reversible drill. I doubt that non-variable speed or single direction drills exist anymore, except as rare pieces of antiquity, but I thought it needs to be said.
* I base this on the fact that I've used a 10 yr old 1/2 hp corded drill (with a keyed chuck) to easily get out a screw that a 20v Dewalt and 3-4 other cordless drills couldn't budge.
Assuming this is a regular Phillips head, you can buy reverse-threaded bits that fit into the stripped part. They grip the screw inside the stripped head and help power it out.
A slightly more radical solution is drilling. You'll need a good metal bit that is at least the diameter of the shaft of the screw. If your screw is protruding (like the picture shows) use an angle grinder with a metal cut-off blade to get the head off, remove whatever you were mounting, and then flush cut it as much as possible. Once it's as flush as you feel comfortable making it, put the bit on the remaining shaft and drill the shaft clean out. Not an easy solution, but I have on occasion gotten one or two stuck this bad and needed the screw gone.
Engineer (a Japanese company) makes a series of pliers specifically designed for screw removal, called the ネジザウルス ("Nejisaurus," lit. "Screwsaurus"). One example is the PZ-58 (English page, Amazon US page). These have ridges or serrations oriented perpendicular to most pliers which allows a better grip for rotating the gripped item around the lengthwise axis, as can be seen on the right in the image below (though to me those "slippage" arrows seem to be pointing in the wrong direction).
There are plenty of video reviews of the PZ-58 on YouTube; this one happens to be the first I found. It points out that the ridges do seem to flatten quite quickly, so it's hard to say how well this will work long-term. But perhaps other manufacturers make similar pliers.
(I have no affiliation or connection with Engineer beyond owning some of their tools. These include a PZ-58, though I've not used it enough to render a serious opinion on them beyond, "from brief use they seem to work better than regular pliers for screw extraction.")
