1. Open your Dashboard and check to see if you have any Widget's installed that might be making animal sounds.
see > Mac Basics: Dashboard gives you quick access to frequently used info
2. Go to: Apple > System Preferences > Sound > Sound Effects and uncheck "Play user interface sound effects"
3. Go to: Apple > Force Quit and Quit any App's that maybe suspect. If you find a suspect and open App at this point, go to: Apple > System Preference > Users & Groups > Login Items and remove it from the list of items that are set to automatically open at login.