In the ancient times, the house has piled high and thick grass, and without woods beneath the grass. This is the only place where animals can warm themselves, therefore, many cats, dogs and other animal, such as mice, rats, and bugs, lived in the grass-roof. When it rains, the roof is smooth, sometimes the animal would slide down from the top of the grass-roof. Thus there is such a saying to describe "the Heavy Rain".

"The much more probable source of 'raining cats and dogs' is the prosaic fact that, in the filthy streets of 17th/18th century England, heavy rain would occasionally carry along dead animals and other debris. The animals didn't fall from the sky, but the sight of dead cats and dogs floating by in storms could well have caused the coining of this colourful phrase."

because of the noise

You really have to be careful when trying to understand certain colourful expressions. Sometimes we really don't know the origin, but it doesn't seem to stop people making up silly theories. I wrote a blog entry about this some months ago about the silly theories behind the phrase. The entry is in Slovak, and that was partly my point: the Slovak equivalent is "tractors are falling"! You can find more equally-quirky phrases from other languages here: http://www.omniglot.com/language/idioms/rain.php We do say "it's bucketing down" or even "it's pissing down"(crass).

A search of usually reliable sources yields only theory and speculation. Ojala, que llueva café.