How can I remove old polls/results in Drupal 7?
You can remove the links by either copying the poll-results--block-tpl.php template file to you theme and removing the line that prints $links or with template_preprocess_poll_results(&amp;$vars) in your template.php file in your theme and removing the line that sets the links variable.

poll-results--block.tpl.php

&lt;div class="poll"&gt;
  &lt;div class="title"&gt;&lt;?php print $title ?&gt;&lt;/div&gt;
  &lt;?php print $results ?&gt;
  &lt;div class="total"&gt;
    &lt;?php print t('Total votes: @votes', array('@votes' =&gt; $votes)); ?&gt;
  &lt;/div&gt;
&lt;/div&gt;


template_preprocess_poll_results(&amp;$vars)

function template_preprocess_poll_results(&amp;$variables) {
  if (isset($variables['vote']) &amp;&amp; $variables['vote'] &gt; -1 &amp;&amp; user_access('cancel own vote')) {
    $elements = drupal_get_form('poll_cancel_form', $variables['nid']);
    $variables['cancel_form'] = drupal_render($elements);
  }
  $variables['title'] = check_plain($variables['raw_title']);

  if ($variables['block']) {
    $variables['theme_hook_suggestions'][] = 'poll_results__block';
  }
}