Cómo filtrar publicaciones por categorías en WordPress

Tengo un custom post type y ahora necesito filtrar los proyectos según sus categorías sin ser redirigido a otra página. También necesito tener una categoría todas que muestre todos los proyectos. Enlace al sitio de prueba. Agradecería cualquier ayuda.

portfolio-type.php:

<?php

if ( function_exists( 'add_theme_support' ) ) { 
   add_theme_support( 'post-thumbnails' );
   set_post_thumbnail_size( 270, 170, true );
   add_image_size( 'screen-shot', 720, 540 );
}

add_action('init', 'portfolio_register');  

function portfolio_register() {
$labels = array(
   'name' => _x('Portafolio', 'post type general name'),
   'singular_name' => _x('Portfolio Item', 'post type singular name'),
   'add_new' => _x('Add New', 'portfolio item'),
   'add_new_item' => __('Add New Portfolio Item'),
   'edit_item' => __('Edit Portfolio Item'),
   'new_item' => __('New Portfolio Item'),
   'view_item' => __('View Portfolio Item'),
   'search_items' => __('Search Portfolio Items'),
   'not_found' => __('Nothing found'),
   'not_found_in_trash' => __('Nothing found in Trash'),
   'parent_item_colon' => ''
);
$args = array(
   'labels' => $labels,
   'public' => true,
   'publicly_queryable' => true,
   'show_ui' => true,
   'query_var' => true,
   'rewrite' => true,
   'capability_type' => 'post',
   'hierarchical' => false,
   'menu_position' => 5,
   'supports' => array('title','editor','thumbnail')
); 
register_post_type( 'portfolio' , $args );
}

function create_portfolio_taxonomies() {
$labels = array(
   'name' => _x( 'Categories', 'taxonomy general name' ),
   'singular_name' => _x( 'Category', 'taxonomy singular name' ),
   'search_items' => __( 'Search Categories' ),
   'all_items' => __( 'All Categories' ),
   'parent_item' => __( 'Parent Category' ),
   'parent_item_colon' => __( 'Parent Category:' ),
   'edit_item' => __( 'Edit Category' ),
   'update_item' => __( 'Update Category' ),
   'add_new_item' => __( 'Add New Category' ),
   'new_item_name' => __( 'New Category Name' ),
   'menu_name' => __( 'Categories' ),
);

$args = array(
   'hierarchical' => true,
   'labels' => $labels,
   'show_ui' => true,
   'show_admin_column' => true,
   'query_var' => true,
   'rewrite' => array( 'slug' => 'categories' ),
);

register_taxonomy( 'portfolio_categories', array( 'portfolio' ), $args );
}
add_action( 'init', 'create_portfolio_taxonomies', 0 );

?>

index.php:

        <!-- Start Portfolio Page -->

    <section id="portfolio" class="page">
        <div class="container">
            <div class="row">
                <div class="span12">

                    <div class="title">Portfoolio</div>
                    <hr>
                    <div class="sub-title visible-desktop">Tööd:</div>

                            <!-- Start Filters -->

                      <?php

                      $taxonomy = 'portfolio_categories';
                      $terms = get_terms($taxonomy);

                      if ( $terms && !is_wp_error( $terms ) ) :
                      ?>
                          <ul class="option-set" data-option-key="filter">
                            <li class="filter-icon hidden-phone">&#0065;</li>
                              <?php foreach ( $terms as $term ) { ?>
                                  <li><a href="<?php echo get_term_link($term->slug, $taxonomy); ?>" ><?php echo $term->name; ?></a></li>
                              <?php } ?>
                          </ul>
                      <?php endif;?>

                        <!-- End Filters -->            

                        <!-- Start Projects -->

                    <div id="posts" class="row isotope">


                      <?php if (have_posts()) : while (have_posts()) : the_post(); ?>  

                          <?php  
                              $title= str_ireplace('"', '', trim(get_the_title()));  
                              $desc= str_ireplace('"', '', trim(get_the_content()));  
                          ?>     

                          <div class="item post item span4 isotope-item">

                            <a class="project-wrp fancybox" title="<?=$title?>" rel="lightbox[work]" href="<?php print portfolio_thumbnail_url($post->ID) ?>"><div class="profile-photo"><div class="profile-icon">&#0102;</div><?php the_post_thumbnail(array('230','170'),array('alt' => '')); ?> </div>  
                            <div class="project-name"><?php echo $title; ?></div>
                            <div class="project-client"><?php echo $desc; ?></div>
                            </a>
                          </div>  
                      <?php endwhile; endif; ?>  

                    </div>

                </div>                    
            </div>
        </div>

    </section>

    <!-- End Portfolio Page -->