How can I sign out of Skype from everywhere logged in to my account?

Solution 1:

Apparently if you change your password and then sign out this will result in the other session being logged out, see: How can I get Skype to log out from another location?

Change your password to make remote Skype clients sign out

1. Go to File | Change Password
2. Follow the instructions to change your password.
3. Now sign out using File | Sign Out
4. Wait a minute or so
5. Then sign in again using your new password.
6. After a short period of time any remote Skype clients that were logged into your Skype username should stop working. They will require the new password in order to log in again.

Solution 2:

According to the help page of Skype, this will do the trick: just type in any chat window

/remotelogout

Sign out all other instances except the current one. This will also stop push notifications on all other instances¹.

To check your current logged in places, run:

/showplaces