Toggle Login / Logout in menu

Source: http://wordpress.stackexchange.com/questions/142342/logout-hyperlink-within-a-sub-menu

Hooks:

// Add a Login hyperlink to the secondary navigation menu if the user is logged-out
function wpa_remove_menu_item( $items, $menu, $args ) {
    if( is_admin() || ! is_user_logged_in() ) return $items;

    foreach ( $items as $key => $item ) {
        if ( 'Login' == $item->title ) unset( $items[$key] );
        if ( 'Logout' == $item->title ){
                 $items[$key]->url=wp_logout_url('your-permalink-to-redirect');
                 /* this will add action to Logout menu item
                    add proper permalink in wp_logout_url to redirect at proper location */
        }
    }

    return $items;
}

add_filter( 'wp_get_nav_menu_items', 'wpa_remove_menu_item', 10, 3 );


// Remove the Logout hyperlink from the secondary navigation menu when the user is logged-in
function wpa_add_menu_item( $items, $menu, $args ) {
    if( is_user_logged_in() ) return $items;

    foreach ( $items as $key => $item ) {
        if ( 'Logout' == $item->title ) unset( $items[$key] );
    }

    return $items;
}

add_filter( 'wp_get_nav_menu_items', 'wpa_add_menu_item', 10, 3 );

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Note: Keep Login & Logout in menu, href for Logout will blank