Logout Redirect and also WP-login.php Redirect

you can do that with this code (paste it to your functions.php)

function auto_redirect_external_after_logout(){
    // check if user is leaving from admin
    // is_admin() check would not work here probably as we left the admin already
    if ( false !== strpos( $_SERVER['HTTP_REFERER'], 'wp-admin' ) ){
        wp_redirect( 'http://www.example-from-admin.com' );
    } else {
        wp_redirect( 'http://www.example-from-front.com' );
    }
    //make sure to call exit after redirect
    exit;
}

//execute the code above on logout
add_action( 'wp_logout', 'auto_redirect_external_after_logout');