The scripts of the owl languages is never really described, apart from one case in The Outcast on page 27, where Coryn is learning to read. He describes the letters R and Y as if they were written in English.
In Legend of the Guardians: The Owls of Ga'hoole, the artists credited South Asian influences when coming up with the writing and visual culture of the owls. In the movie, Hoolian script bares similarities to Chinese calligraphy, Mongolian script and Balinese. The lines are read from top to bottom like Chinese, but the page is read from left to right, like English.
It is unlikely the script created for the movie is a functional language. In some cases, the script is actually stylized English.
It is assumed that the Owl Kingdoms at one point spoke one language, being split off from the same ancestral bird. Traces of this language seem to be difficult to concoct, as the closest languages we have are Krakish, which seems to be Germanic/Slavic in grammar and phonology, and Jouzhen, which seems to be based off of Chinese/Asiatic tonal languages.