The first TVtropes link I put has a list of the "episodes" that have been documented by readers so far. Each chapter seems to be its own episode of sorts.
The plot itself is not very interesting, the only thing noteworthy about the plot is all the bizarre and absurd things that occur in it, but it is not fun to read. You can see examples of the strange things that happen in the story on TVtropes.
As far as I can tell, there are no fanfics of this particular work, but there is a lot of fan fiction of the Loud House.