I'm on version 22.214.171.124 - here's how to sign off:
At the top of the Contacts list (compact view mode) or above your name (default view) there is a row of commands: Skype Contacts Call View Tools Help
Click on Skype -> Sign Out.
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-> Good reads: Devise good passwords and stop password attacks
and this one, too: http://www.rd.com/slideshows/internet-security-how-not-to-get-hacked/