Add this code in your function.php. it will automatically add login-logout link in your menu
add_filter('wp_nav_menu_items', 'add_login_logout', 10, 2);
function add_login_logout($items, $args) {
$loginoutlink = wp_loginout('index.php', false);
$items .= '<li>'. $loginoutlink .'</li>';
return $items;
}