Updated answer:
Use two floated lists to emulate columns, same approach as previously though.
<?php
/*
Template Name: PageOfPosts
*/
get_header(); ?>
<div id="content">
<div class="t">
<div class="b">
<div class="l">
<div class="r">
<div class="bl">
<div class="br">
<div class="tl">
<div class="tr">
<div class="pad">
<?php while( have_posts() ) : the_post(); ?>
<?php
$category = get_post_meta( get_the_ID(), 'category', true);
$img_style="style="width:606;height:34;position: absolute; padding-top:1px; padding-left: 2px; z-index:9999; background: no-repeat;"";
?>
<div class="post" id="post-<?php the_ID(); ?>">
<h1><?php the_title(); ?></h1>
<img src="https://wordpress.stackexchange.com/questions/13209/wp-content/themes/DD4L/images/leafhr.png" <?php? echo $img_style;?>>
<br />
<div class="entry">
<?php the_content(); ?>
<?php wp_link_pages(array('before' => 'Pages: ', 'next_or_number' => 'number')); ?>
</div>
<?php edit_post_link('Edit this entry.', '<p>', '</p>'); ?>
</div>
<?php endwhile; ?>
<br /><br />
<?php if( !empty( $category ) ) : ?>
<?php
$args = array(
'orderby' => 'title',
'order' => 'asc',
'nopaging' => true,
'ignore_sticky_posts' => true,
'tax_query' => array(
array(
'taxonomy' => 'category',
'terms' => array( $category ),
'field' => 'slug'
)
)
);
$category_query = new WP_Query( $args );
?>
<?php if( $category_query->have_posts() ) : ?>
<?php
$total = $category_query->post_count;
$quart = $total / 4;
if( floor( $quart ) != $quart )
$quart = ceil( $quart );
$counter = 0;
?>
<div class="float-container">
<ul class="alignleft">
<?php while( $category_query->have_posts() ) : $category_query->the_post(); $counter++; ?>
<li>
<a href="https://wordpress.stackexchange.com/questions/13209/<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a>
</li>
<?php if( $quart == $counter ) : $counter = 0; ?>
</ul>
<ul class="alignleft">
<?php endif; ?>
<?php endwhile; ?>
</ul>
<div class="clear"></div>
</div>
<?php endif; ?>
<?php endif; ?>
</div>
<div class="clear"></div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<?php get_sidebar(); ?>
<?php get_footer(); ?>
See edit revision for previous comments and code.