Is there a method to calculate something like general \"similarity score\" of a string? In a way that I am not comparing two strings together but rather I get some number/scores
Have a look at locality-sensitive hashing.
The basic idea is to hash the input items so that similar items are mapped to the same buckets with high probability (the number of buckets being much smaller than the universe of possible input items).
There's a very good explanation available here together with some sample code.