exit out of all SSH connections in one command and close PuTTY

Try using the ssh connection termination escape sequence.

In the ssh session, enter ~. (tilde dot). You won't see the characters when you type them, but the session will terminate immediately.

$ ~.
$ Connection to me.myhost.com closed.  

From man 1 ssh

The supported escapes (assuming the default ‘~’) are:
 ~.      Disconnect.
 ~^Z     Background ssh.
 ~#      List forwarded connections.
 ~&      Background ssh at logout when waiting for forwarded 
         connection / X11 sessions to terminate.
 ~?      Display a list of escape characters.
 ~B      Send a BREAK to the remote system (only useful for SSH protocol
         version 2 and if the peer supports it).
 ~C      Open command line.  Currently this allows the addition of port 
         forwardings using the -L, -R and -D options (see above). It also
         allows the cancellation of existing remote port-forwardings using 
         -KR[bind_address:]port.  !command allows the user to execute a 
         local command if the PermitLocalCommand option is enabled in
         ssh_config(5).  Basic help is available, using the -h option.
 ~R      Request rekeying of the connection (only useful for SSH protocol 
         version 2 and if the peer supports it).

Just press CtrlD and it will log you out there for hold ctrl and press "d" till the window disappears.

Simply close PuTTY. (Alt+F4 by default IIRC.)