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

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

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.