Now Opera has updated settings and you can easily set up automatic deleting all cookies and other site data, browsing history, download history, cached images and files, passwords and other sign-in data, autofill form data, site settings, and hosted app data automatically on exit.
To do it you need:
Open Settings (Alt+P).
Under Privacy and Security, select Delete browsing data and click the On exit section.
Choose the data you want to have deleted every time you exit Opera.
Click Save, and you’re all set.