Buy another. The OM-20 (OM-G in the USA) is cheap used. I see them all the time for $20.
I have a soft spot for this camera because my first manual camera was an OM-G that my dad bought me when I was 11 years old. Still, they were not a very well-made camera compared to Olympus's pro models like the OM-2, which is very cheap used now, too, and is a much better camera.
Thank you, for your reply. I realize that this cameras are quite cheap nowdays and it makes more sence to buy a new one, then to work on this particular unit. However, I want to try to fix it by my self, cause it seems to be interesting challenge)
My main working horse is OM-1n, so I don't really have a big interest about this OM20, but will be happy to get it to live with my own hands.
I believe that this is the result of dirty shutter magnets. Cleaning them involves removing the bottom part of the mirror box.
Here is a tutorial about OM10 _should be the same.
https://youtu.be/oF3_OelqSWM
Send a PM to John Hermanson. He's an RFF member who was Olympus's Service Manager in the USA for many years. He retired and started his own repair business specializing in the OM system. He could give you an idea of what you would need to do, and if its something you can do.
First thing I'd be doing is checking inside the guide rails for something obstructing movement of the shutter curtain ... it may just be that simple!