This is not really a WordPress Question, as you made a basic PHP mistake, but I’ll help you anyway 😉
you forgot to close the conditional with an }
before the elseif
statements.
This should work:
<ul>
<?php if (get_post_meta($post->ID, 'hm_check_image1', true)) { ?>
<li>
stufff stuff other meta info...
</li>
<?php } else if (get_post_meta($post->ID, 'hm_check_image2', true)) { ?>
<li>
stufff stuff other meta info...
</li>
<?php } else if (get_post_meta($post->ID, 'hm_check_image3', true)) { ?>
<li>
stufff stuff other meta info...
</li>
<? } else { ?>
<!--no checkbox ticked-->
<?php } ?>
</ul>