query_posts that have custom taxonomy and limiting what shows based on the taxonomy

You have lot of issues here;

• Never ever use query_posts, it breaks the main query and page functionalities.

• You are breaking and nullifying the main query even before query_posts can have a change to do it in this line $wp_query= null

• As this is a shortcode (taken from your comments) and with this line, 'posts_per_page' => $num,, I believe that you are using extract(). You should never use extract() as it is almost un-debuggable, unreliable and fails silently. For this reason it was removed from core functions`

• The correct value to orderby to sort by post date is date, not post_date. This is the default, so you can just omit this as you are not modifying it through an attribute. This also goes for offset and order

• You need to use a tax_query to get posts from a specific term

Here is a small example you can work from. (Please note, you should sanitize and validate all user inputs. I have not done any of that).

add_shortcode( 'my_shortcode', function ( $atts )
{
    $attributes = shortcode_atts(
        [
            'numberposts' => 10, // Default amount of posts to show
            'post_type'   => 'technologies', // Default post type
            'taxonomy'    => 'importance', // Default taxonomy
            'terms'       => 'featured' // Default term to exclude
        ],
        $atts, 
        'my_shortcode' 
    );

    $paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
    $args = [
        'posts_per_page'   => $attributes['numberposts'],
        'post_type'        => $attributes['post_type'],
        'tax_query'        => [
            [
                'taxonomy' => $attributes['taxonomy'],
                'field'    => 'slug',
                'terms'    => $attributes['terms'],
                'operator' => 'NOT IN' // This will exclude all posts with terms set in 'terms'
            ]
        ],
        'post_status'      => 'publish',
        'paged'            => $paged,
        'suppress_filters' => true
    ];
    $q = new WP_Query( $args );

    $output="";
    if ( $q->have_posts() ) {
        while ( $q->have_posts() ) {
            $q->the_post();

            $output .= apply_filters( 'the_title', get_the_title() );

        }
        $output .= get_next_posts_links( 'Next', $q->max_num_pages );
        $output .= get_previous_posts_links( 'Previous' );
        wp_reset_postdata();
    }
    return $output;
});

You can just call it as [my_shortcode] if you don’t need to change the defaults

FINAL NOTES

• I assumed that you would want to exclude the featured term, so I have written the tax_query around that.

• You will need PHP5.4+ as the code uses the new short array syntax ([]). If you have an older version, just change to the old array syntax (array()). Just be sure then you have at least PHP 5.3 to support the closure used