JohnnyPea

This plugin adds enhanced “Navigation Menu” widget. It offers many options which could be set to customize the output of the custom menu through the widget.
Features include:
<ul>
<li>Custom hierarchy – “Only related sub-items” or “Only strictly related sub-items”.</li>
<li>Starting depth and maximum level to display + flat display.</li>
<li>Display all menu items starting with the selected one.</li>
<li>Display only direct path to current element or only children of selected item (option to include the parent item).</li>
<li>Display menu as drop down.</li>
<li>Custom class for a widget block.</li>
<li>And almost all the parameters for the <a href="https://codex.wordpress.org/Function_Reference/wp_nav_menu" rel="nofollow ugc">wp_nav_menu</a> function.</li>
<li>shortcode <code>[advMenu]</code></li>
<li>Display menu items descriptions.</li>
</ul>
Are you missing something or isn’t it working as expected ? I am open to suggestions to improve the plugin !
Thanks the <a href="http://wp.sk/" rel="nofollow ugc">Slovak WordPress community</a> and <a href="http://www.webikon.sk/" rel="nofollow ugc">Webikon</a> for the support. For more information about me check out my <a href="http://bocinec.sk/" rel="nofollow ugc">personal page</a>.
<h3>Options</h3>
<ul>
<li>“Title” – set the title for your widget</li>
<li>“Custom Widget Class” – custom class for widget block</li>
<li>“Select Menu” – menu from the custom menus you want show</li>
<li>“Show hierarchy” – you can set to display only related or strictly related items</li>
<li>“Starting depth” – display only menu items which depth is greater then this</li>
<li>“How many levels to display” – limit the display from 1 to 5 levels or flat display</li>
<li>“Filter selection from” – only items which are children or grandchildren of selected element will be displayed</li>
<li>“Select the filter” – filter the direct path for the current menu item (like breadcrumb navigation) or display only its children</li>
<li>“Include parents” – when checked it display also parent item upon filters (e.x. Display only children of selected item)</li>
</ul>
<h3>Shortcode</h3>
You can use <code>[advMenu]</code> shortcode with the parameters listed below:
<pre><code>'nav_menu' (menu ID) 
'title' 
'dropdown' 
'only_related' 
'depth' 
'container' 
'container_id' 
'menu_class' 
'before' 
'after' 
'link_before' 
'link_after' 
'filter' 
'filter_selection' 
'include_parent' 
'start_depth' 
'hide_title' 
'custom_widget_class'
</code></pre>
e.g. <code>[advMenu title="Menu Title" nav_menu=2]</code>

Advanced Menu Widget

David Mosterd

Tobias Schutter

Uses the native <a href="https://codex.wordpress.org/Function_Reference/wp_nav_menu" rel="nofollow ugc">wp_nav_menu()</a>. Add parameters to the wp_nav_menu() to enable functionality. 
Also, ships with one-click delete menu-items in the WordPress admin. Turned off or on using the screen-options. Sweet.
Examples
This will get the first sub-menu from the active branch and 2 levels beyond (menu + sub-menu + sub-menu):
<pre><code>wp_nav_menu( array(
 'level' => 2,
 'depth' => 3
));
</code></pre>
Show the current branch only:
<pre><code>wp_nav_menu( array(
 'level' => 1
));
</code></pre>
Aimed on simple use in various use cases:
<pre><code>// display first level in the header
wp_nav_menu( array(
 'depth' => 1
));

// display first sub-menu from the current branch somewhere else
wp_nav_menu( array(
 'depth' => 2,
 'level' => 2
));
</code></pre>
Another feature is it’s control over the css classes that are given to a menu-item. You might be faced with css selectors 
which you cannot change. The ‘codepress_menu_filter_classes’ filter can be used in your functions.php to set the class property:
<pre><code>/**
 * Change the classes of a menu item
 *
 * @param array $classes List current classes
 * @param object $item Current menu item
 * @param array $items Current list of items (per level)
 * @param integer $k Key of the current item in $items
 */
function codepress_menu_item_classes( $classes, $item, $items, $k ) {
 // mark the first item
 if ( reset( $items ) == $items[ $k ] )
 $classes[] = 'first';

 // mark the last item
 if ( end( $items ) == $items[ $k ] )
 $classes[] = 'last';

 // map the WordPress default 'current-menu-item' class to 'active'
 if ( in_array( 'current-menu-item', $classes ) )
 $classes[] = 'active';

 return $classes;
}
add_filter( 'codepress_menu_item_classes', 'codepress_menu_item_classes', 10, 4 );
</code></pre>
Simple Menu Delete
It ships with one-click delete menu-items within WordPress. 
This functionality was integrated from our Simple Menu Delete plugin and enhanced a bit:
<ul>
<li>Turned off or on using the screen-options.</li>
<li>Display is more in line with WordPress’s way of delete-links.</li>
<li>Works exactly the same now as the nested delete-link which is a click further inside the menu item.</li>
</ul>

Codepress Menu

Allows you to display a sub-menu, it's depth from there on and gives you control over the menu-item classes.

Advanced Menu Widget vs Codepress Menu