The deletion option from the menu is unfortunately quite unclear. It's called 'close' (including deletion of your data), 'deactivate' and 'suspend'. However this is merely deactivation. For that, try this link: http://www.sonico.com/cancel.php
If you signed up for Sonico using a third-party login such as Facebook or Twitter, you probably want to revoke all access from Sonico. Click the icon below to find out how.