When getting on my bike I stood on the left pedal and my full weight caused the pedal to skip a thread. The pedal is now squinted and stuck in the crank. The pedals were cheap, but I am hoping to continue using the cranks. Does anyone know a good way to remove the pedal without destroying the crank? I was thinking of trying to drill it out and re-tap the crank but I would rather not if I can avoid it. Many thanks in advance.
The most likely cause of what happened is the pedal was installed with insufficient torque. This can allow movement in the threads that degrades the crank threads, which are aluminum in most cases and will wear away readily even as the hardened steel pedal threads remain intact. This all being the case, it's likely there's already damage to the crank threads no matter what you do from here. (Even if it were a steel crank, it still wouldn't be as hard and wear-resistant as the hardened material of the pedal spindle).
You could try to minimize damage to the crank by leveraging the pedal back into alignment before unscrewing it. It's possible that works out in your favor compared to driving the pedal out in a cross-threaded orientation. It could also do all sorts of damage itself if attempted. I have seen some pedals that are very low end and/or borderline defective where the threads are badly formed with blunt as opposed to sharp, crisp tips, causing the major diameter of the thread form to not really be what it's supposed to be; this isn't common but if it were the root cause of problem, then forcing the pedal back into position might work.
Ultimately the thread will likely need to be repaired afterward no matter what, which can be done by chasing with a tap if the damage is moderate or only affects a few threads, or installing a helical insert (helicoil) if the threads are toast.
How did you know it skipped a thread?
Pedals become very, very tight even in normal usage. The fact that it's almost impossible to remove a pedal doesn't mean it skipped a thread.
Here are some instructions for pedal removal: https://yarchive.net/bike/pedal_remove.html
Once pedals have gotten beyond the removal with a regular pedal wrench by hand, they are often too tight to be safely removed without heat. If you were to force them off, assuming you had a wrench and sufficient force, you would probably damage the threads in the crank and possibly the pedal because aluminum would weld to the steel pedal thread during removal.
Remove the crank and heat the pedal end of the aluminum over the kitchen stove or equivalent. When the crank is hot enough to sizzle when touched with a wet finger, use the wrench and it should come off about the way a lubricated tight pedal usually does. If you have a torch and try this on the bicycle, it is not easier, because you can't hold the crank as well.
Note you need a true pedal wrench. Nothing else will remove your pedal, not cone wrench (too weak), not normal open ended wrench (not long enough, too wide). If your pedal is one of those with an Allen wrench without flats, it may be impossible to remove it (you may destroy the Allen wrench or the hex head on the pedal), because Allen wrench limits the maximum torque to a very low value. But you could still try with a long high quality Allen wrench and a cheater bar.
More instructions: https://www.sheldonbrown.com/brandt/stuck-pedals.html
Also note that pedals have opposing orientations. So if you removed right pedal and can't remove the left, it may be possible you are actually tightening the left pedal, not loosening, because the left pedal has strange thread orientation.
Don't drill it out, you'll destroy your cranks.
Remember that heat heals. Heating the crank with a gas stove or a similar flame can do wonders and what couldn't be moved before can often move with that. I assumed that your cranks are not made of carbon fiber. Do that if the biggest leverage you can do fails. A metal pipe bar put on your wrench to extend it can help you to provide very large leverage.
When trying to use all my power (which is not that big, I do not wight much) I was most successful by placing the wrench in such a way that I could step on it forcefully. That means, below the crank. Be extra careful not to injure yourself. It is better of the chain is on the large chainring and covers the teeth.
Always think about the correct direction of rotation. I suggest the right hand rule (for the right pedal), and the left hand rule (for the left pedal) respectively. When you rotate in the direction where your fingers are pointing, you are forcing the screw to move in the direction of your thumb. It is much more useful than some righty tighty especially when your native language is not English. Also, do not get confused by hex keys that are inserted from the other side, the rule is still valid, you need the pedal to go away from the crank and away from the frame.
Drilling and Retapping a thread into a crankarm is the very-last step before buying replacement cranks.
It can be done by a well outfitted workshop, using a mill and the correct taps, but against you are 3 problems:
Pedal axles are hardened - even the cheap ones are surface hardened and getting then to drill with home tools is a challenge.
The thread specs of a pedal are uncommon. 9/16 inch and 20 TPI, plus you need a left-hand tap on one side. These are only used on pedal threads, so are exclusive to the bike industry.
Thread Replacements ("Helicoils tm") are also expensive for this spec - again the more-common 18 TPI thread is cheap, but the pedal-specific 20 TPI is expensive.
I suspect your pedal's axle has bent rather than slipping out. They are generally hard to get straight and if they were only cheap to begin with then replacement might be easiest.
Removal Use a pedal spanner if you can - an adjustable spanner tends to be too wide in many places. Some pedals only offer a hex socket on the inboard end, but that's generally fancy ones only.
Set the bike like you're about to push off and ride. The pedal to be removed should be forward, and slightly above the axle. Set your tool on the flats so that the handle pokes up and you can press it with your heel while the ball/toes are on the pedal.
Use hot air on the end of the crank, and after 20~30 seconds of heating douse the pedal axle only with WD40 or CRC556 or similar. This is to gently heat the crank while cooling the shaft.
Then get on the bike and push the tool down with your heel while your toes are on the pedal.
Main reason for this is leverage, but it also gets the thread direction correct.