How can I find out who sent me bitcoins? I had a very unusual situation. I received the bitcoins in my wallet, how can I find out who sent them?

Maybe it was the Creator of bitcoin ? :)
how can I find out who sent them? 


Realistically, you cannot. You could see which inputs were used in the transaction that sent you the bitcoins, and attempt to find their owner. But there is no information encoded into the transaction that states who sent it.

If you met someone that claimed they were the one to send the coins to you, then you could ask them to sign a specific message of your choosing, with the private key of one of the transaction's inputs. Whoever sent the coins to you will have access to at least one of those private keys, so they would be able to prove themselves in this way.