I would suggest the following:
Take the PSU out again, so the case is not in the way. Try to get the screws into the holes in the PSU by hand, if they fit and the thread is ok, that should go smoothly. If the thread is badly made or slightly damaged by your workings, you might encounter a bit of resistance but not much at that diameter. Maybe overcome that with the careful help of a screwdriver, but make sure you are actually doing good (right alignment, right size). You would be basically "recutting" parts of the thread so they match up with the rest. If it doesn't feel right, cancel it. Dismiss the screws and see below.
If the screws really only go in a tiny bit like in your picture, you most likely have the wrong screws (too big or wrong threading) for some reason. If you can, try different ones, maybe your case came with a bag of spares (kinda likely).
Once you know you have the correct screws, use them to screw that PSU (into your case). ;-)
bonne chance, good luck