Where can I find stories about Moomins in Finnish language? (on-line). Thank you.

The Moomin books are not available on on-line. In case you live in Helsinki (or elsewhere in Finland) you can visit the nearest library and borrow those books. The first Moomin book is called "Muumit ja suuri tuhotulva" in Finnish (originally written in Swedish). You can check the library items of the Helsinki metropolitan area public libraries from the HelMet-catalogue: http://www.helmet.fi/screens/opacmenu.html