You could use a custom query to fetch the product object. Here is a snippet to get the stock count. Take a look at the product class: http://docs.woothemes.com/wc-apidocs/class-WC_Product.html for functions available for the product object.
<?php $args = array(
'post_type' => 'product',
'post_status' => 'publish',
'posts_per_page' => -1,
'orderby' => 'title',
'order' => 'ASC',
'tax_query' => array(
array(
'taxonomy' => 'product_type',
'field' => 'slug',
'terms' => array('simple'),
'operator' => 'IN'
)
)
);
$loop = new WP_Query( $args );
$stock_count = array();
while ( $loop->have_posts() ) : $loop->the_post();
global $product;
$stock_count[] = $product->get_stock_quantity();
endwhile;
// count the array values and output them
echo "<h2>Stock Count: ".array_sum($stock_count)."</h2>";
?>