I have a 15 sqm "friggebod" where one of the doors is misaligned, preventing it from closing properly. I haven't been concerned about it before, partly because we only store tools, etc. here, but mostly because it's more of a cosmetic issue. However, in connection with repainting, I thought I would fix it. The simplest solution would be to loosen the hinges and just move the door up a few centimeters - the problem is that I suspect the door might slide back into the old screw holes, as the screws are relatively large and the door weighs quite a bit. Is there any extra strong chemical wood or sealant that could work? In this case, it's mainly not just about sealing the holes, but primarily that the filling should be strong enough since the screw holes are so close to each other.
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Buy a tube of adhesive. Fill the old holes with the caulking gun and let it dry...if it doesn't work with washers.
Drill up and glue wooden dowels into the old screw holes.
OK, thank you for all the help - feels like I have several good options to go for now! 
Finally went with the suggestion of a dowel + glue, so now I have a working door again. Thank you