How can I sort the order of multiple custom field values in a custom post type?

the function the_meta() formats the data into an unordered list and you have no control over the order. Instead you should use get_post_custom() and echo out only the fields you want and in the order you want.

change:

<?php echo(the_meta()); ?>

to :

    $post_custom =  get_post_custom($post->ID);
    echo '<ul>';
    echo '<li>'.$post_custom['Height'].'</li>';
    echo '<li>'.$post_custom['Fueled_By'].'</li>';
    echo '<li>'.$post_custom['Favorite_Quote'].'</li>';
    echo '<li>'.$post_custom['Areas_of_Expertise'].'</li>';
    echo '</ul>';

and change the name of the fields to match yours.