The only function of statues, other than making your city more attractive, is to raise the desirability of the area. Increasing the desirability of the area is sometimes necessary to evolve housing to a higher level. Large statues have a greater effect than medium statues, which have a greater effect than small statues.
Statues do not affect the Gods. To keep the Gods happy, you need to build shrines, temples, and/or a temple complex. Festivals to the Gods also please them. The Patron God is twice as hard to please as the local Gods.
VAIA