[Add Login/Logout Link to Menu] #MenuPanel

functions.php

function gl_loginout_menu_link( $items, $args ) {
   if ($args->theme_location == 'primary') {
      if (is_user_logged_in()) {
         $items .= '<li class="right"><a href="'. wp_logout_url() .'">'. __("Log Out") .'</a></li>';
      } else {
         $items .= '<li class="right"><a href="'. wp_login_url(get_permalink()) .'">'. __("Log In") .'</a></li>';
      }
   }

   return $items;
}
add_filter( 'wp_nav_menu_items', 'gl_loginout_menu_link', 10, 2 );

login logout panel in menu page

<?php

/* 
 * To add a metabox in admin menu page 
 */
function d2l_add_custommenu_metabox() {
	add_meta_box( 'add-d2l_custommenu', __( 'Register, Log In/Out Links' ), 'd2l_custommenu_metabox', 'nav-menus', 'side', 'default' );
}
add_action( 'admin_head-nav-menus.php', 'd2l_add_custommenu_metabox' );

/*
 * The metabox code. 
 */
function d2l_custommenu_metabox( $object ) {
	global $nav_menu_selected_id;
	
	$menukeywords = array(
		'#d2l_login#'    => __( 'Log In' ),
		'#d2l_logout#'   => __( 'Log Out' ),
		'#d2l_loginout#' => __( 'Log In/Out' ),
		'#d2l_register#' => __( 'Register/Sign Up' ),
		'#d2l_profile#'  => __( 'Profile' )
	);
	
	class d2lCustomMenuItems {
		public $db_id = 0;
		public $object = 'd2l_custommenu';
		public $object_id;
		public $menu_item_parent = 0;
		public $type = 'custom';
		public $title;
		public $url;
		public $target = '';
		public $attr_title = '';
		public $classes = array();
		public $xfn = '';
	}
	
	$menukeywords_obj = array();
	foreach ( $menukeywords as $value => $title ) {
		$menukeywords_obj[ $title ]            = new d2lCustomMenuItems();
		$menukeywords_obj[ $title ]->object_id = esc_attr( $value );
		$menukeywords_obj[ $title ]->title     = esc_attr( $title );
		$menukeywords_obj[ $title ]->url       = esc_attr( $value );
	}
	$walker = new Walker_Nav_Menu_Checklist( array() );
	?>
	<div id="d2l-custommenu" class="loginlinksdiv">
		<div id="tabs-panel-d2l-custommenu-all" class="tabs-panel tabs-panel-view-all tabs-panel-active">
			<ul id="d2l-custommenuchecklist" class="list:d2l-custommenu categorychecklist form-no-clear">
				<?php echo walk_nav_menu_tree( array_map( 'wp_setup_nav_menu_item', $menukeywords_obj ), 0, (object) array( 'walker' => $walker ) ); ?>
			</ul>
		</div>
		
		<p class="button-controls">
              <span class="list-controls">
                    <a href="<?php echo admin_url( '/nav-menus.php?d2l_custommenu-tab=all&amp;selectall=1#d2l-custommenu' ); ?>" class="select-all aria-button-if-js" role="button">Select All</a>
              </span>
			<span class="add-to-menu">
                    <input type="submit"<?php disabled( $nav_menu_selected_id, 0 ); ?> class="button-secondary submit-add-to-menu right" value="<?php esc_attr_e( 'Add to Menu' ); ?>"
                           name="add-d2l-custommenu-menu-item" id="submit-d2l-custommenu"/>
                    <span class="spinner"></span>
              </span>
		</p>
	</div>
	<?php
}

/*
 * Replace the #keyword# by links 
 */
function d2l_setup_nav_menu_item( $menu_item ) {
	global $currentpage;
	
	$menukeywords = array( '#d2l_login#', '#d2l_logout#', '#d2l_loginout#', '#d2l_register#', '#d2l_profile#' );
	
	if ( isset( $menu_item->object, $menu_item->url )
	     && $currentpage != 'nav-menus.php'
	     && ! is_admin()
	     && 'custom' == $menu_item->object
	     && in_array( $menu_item->url, $menukeywords ) ) {
		
		$item_url = substr( $menu_item->url, 0, strpos( $menu_item->url, '#', 1 ) ) . '#';
		
		$item_redirect = str_replace( $item_url, '', $menu_item->url );
		
		if ( $item_redirect == '%actualpage%' ) {
			$item_redirect = $_SERVER['REQUEST_URI'];
		}
		
		switch ( $item_url ) {
			case '#d2l_login#'    :
				$menu_item->url = wp_login_url( $item_redirect );
				break;
			case '#d2l_logout#'   :
				$menu_item->url = wp_logout_url( $item_redirect );
				break;
			case '#d2l_profile#'   :
				if ( is_user_logged_in() ) {
					$current_user     = wp_get_current_user();
					$menu_item->title = 'Hi, ' . $current_user->display_name;
					$menu_item->url   = get_edit_user_link( $current_user->ID );
				} else {
					$menu_item->title = '#d2l_profile#';
				}
				break;
			
			case '#d2l_register#' :
				if ( is_user_logged_in() ) {
					$menu_item->title = '#d2l_register#';
				} else {
					$menu_item->url = wp_registration_url();
				}
				break;
			
			case '#d2l_loginout#' :
				if ( is_user_logged_in() ) {
					$menu_item->title = 'Log Out';
					$menu_item->url   = wp_logout_url();
				} else {
					$menu_item->title = 'Log In';
					$menu_item->url   = wp_login_url();
				}
				break;
		}
		
		$menu_item->url = esc_url( $menu_item->url );
	}
	
	return $menu_item;
}
add_filter( 'wp_setup_nav_menu_item', 'd2l_setup_nav_menu_item' );

function d2l_nav_menu_objects( $sorted_menu_items ) {
	foreach ( $sorted_menu_items as $k => $item ) {
		if ( $item->title == $item->url && '#d2l_register#' == $item->title ) {
			unset( $sorted_menu_items[ $k ] );
		}
		
		if ( $item->title == $item->url && '#d2l_profile#' == $item->title ) {
			unset( $sorted_menu_items[ $k ] );
		}
		
	}
	
	return $sorted_menu_items;
}
add_filter( 'wp_nav_menu_objects', 'd2l_nav_menu_objects' );