order and looping through query

I have a query to loop thorough all the posts in a particular category. Each post is also assigned to another category. I’m able to output each post with just its alternate category, but need posts grouped by their category (not listed each time), and also I need to order the categories.

Here’s the current code (volume-4-number-1 is the slug for category 21):

<?php

query_posts(array('category_name' => 'volume-4-number-1', 'posts_per_page' => -1 )); 

while ( have_posts() ) : the_post();
        echo '<li>';

	foreach((get_the_category()) as $cat) {
    	if ($cat->cat_ID !='21')
       	echo '<a href="'.get_category_link($cat->cat_ID).'">' . $cat->cat_name . '</a>';
}
	echo '<br />';
	the_title();
	echo '</li>';
endwhile;
// Reset Query
wp_reset_query();

?>

SO, I need to have the category name, then below show each post in the category.

I also need to order the category names. SO, out put should be:

Category 1
post
post
post
Category x
post post

Right now it’s
Category 1
post
Category 1
post
Category 1
post
Category x
post
Category x
post

Can someone please help?

Thanks!