Who Invented The Words Er, Um And Ah? Did It Just Pop In Their Mouths?

Those are called disfluencies and most likely originated spontaneously, as you suggest.  As we reach for the next word or line of thought, some feel it necessary to fill the space with a sound.  Once these disfluencies are introduced, they tend to propagate into mainstream usage.  

They are similar to discourse markers (e.g., You know, I mean).