How do I override recurring text/strings with icons/images? I'm not sure this is possible or if there is a module that does this already, that's why I am asking :) Think of String Overrides except to turn strings into an image.

I ran into the module Iconify which basically adds icons to the admin config headings, and I was wondering if there is a way to use icons/images to replace specific recurring strings. For example:
Say I would like to change the "View" link on the Page content type into an icon of an eye. Or the "Edit" link into a little pencil.

How can I achieve what I am trying to do?
Drupal allows you to override almost anything and what you are referring to here is the theme()ing of various pieces.  In your specific example, 'View' and 'Edit' are tabs/local tasks on a node page, and they are themed something like this in Drupal 6:

/**
 * Generate the HTML output for a single local task link.
 *
 * @ingroup themeable
 */
function theme_menu_local_task($link, $active = FALSE) {
  return '&lt;li '. ($active ? 'class="active" ' : '') .'&gt;'. $link ."&lt;/li&gt;\n";
} 


and this in Drupal 7:

/**
 * Returns HTML for a single local task link.
 *
 * @param $variables
 *   An associative array containing:
 *   - element: A render element containing:
 *     - #link: A menu link array with 'title', 'href', and 'localized_options'
 *       keys.
 *     - #active: A boolean indicating whether the local task is active.
 *
 * @ingroup themeable
 */
function theme_menu_local_task($variables) {
  $link = $variables['element']['#link'];
  $link_text = $link['title'];

  if (!empty($variables['element']['#active'])) {
    // Add text to indicate active tab for non-visual users.
    $active = '&lt;span class="element-invisible"&gt;' . t('(active tab)') . '&lt;/span&gt;';

    // If the link does not contain HTML already, check_plain() it now.
    // After we set 'html'=TRUE the link will not be sanitized by l().
    if (empty($link['localized_options']['html'])) {
      $link['title'] = check_plain($link['title']);
    }
    $link['localized_options']['html'] = TRUE;
    $link_text = t('!local-task-title!active', array('!local-task-title' =&gt; $link['title'], '!active' =&gt; $active));
  }

  return '&lt;li' . (!empty($variables['element']['#active']) ? ' class="active"' : '') . '&gt;' . l($link_text, $link['href'], $link['localized_options']) . "&lt;/li&gt;\n";
}


So, to change this from text to a graphic, you would create a theme function of your own in your theme's template.php file:

function YOURTHEME_menu_local_task(....


that looked at either $link or $variables['#link'] and output an image instead of the text.

And if php isn't your forte, but jQuery is, you could also do it in the browser with something like:

$('.tabs a[href$="edit"]').html('&lt;img src="edit.jpg"&gt;');


which would replace the text of your edit link with an image.  If you went this route you would put this in a suitable drupal behavior wrapper in your theme or custom module as well.