I believe it can have two interpretations:
1) Mr. Nobody is the person who gets blamed for everything that goes wrong in the house, but he’s really imaginary. It’s the people in the house doing the “bad” things, but they blame it on Mr. Nobody.
2) Mr. Nobody is an elf sort of figure from mythology. They are known to make mischief. I saw this song in my daughter’s piano book and it had a picture of a little elf-like man.