Set colors depending on category

by

Setting aside that you’re incorrectly using query_posts(), the easiest solution is to add a call to post_class(), to output post-specific classes, including .category-{ID} and .category-{slug}:

<?php if ( have_posts() ) while ( have_posts() ) : the_post(); ?>
    <li <?php post_class(); ?>><a href="https://wordpress.stackexchange.com/questions/123066/<?php the_permalink(); ?>" title="<?php the_title(); ?>"><strong><?php the_title(); ?></strong></a><br />
    <em><?php echo substr(get_the_excerpt(), 0,110); ?> ...</em>
    </li>
    <br />
<?php endwhile; ?>

Then, you can use CSS to target li.category-{ID}.