How strong is XOR encryption of 256 bit plain text with 256 bit key? I was wondering if we take just 256 bits of plain text and simply XOR  every bit with a 256 bit key, how strong can it be ?
That construction is called a one-time pad or OTP (not to be confused with a one-time password). OTP's are theoretically perfectly secure as long as the key is not repeated or reused and the key is indistinguishable from random by any adversary. In that case any 256 bit plaintext message is equally likely, so it is impossible to even brute force the key. Because of that, the size of the key and plaintext do not even matter, as long as there are as many bits for the key as there are bits in the plaintext.

Note that an OTP does not provide message integrity nor authenticity, only confidentiality. Of course the exact size of the input is leaked by an OTP too, so that's not kept secure either.

Of course, generally the practical security depends on the system, the quality of the randomness, the actual access to the key etc. etc. etc.