How can I modify body class based on non-taxonomy node data?
You could do this in your theme's template.php. Something like this:

function mytheme_preprocess_html(&amp;$vars) {

  // Load node
  $node = menu_get_object();
  if ($node) {

    // Wrap to fetch field values easily 
    $wrapper = entity_metadata_wrapper('node', $node);

    // Check image reference fields and add body class
    if (
      $wrapper-&gt;field_featured_image-&gt;raw() ||
      $wrapper-&gt;field_image_gallery-&gt;raw()
    ) {
      $vars['classes_array'][] = 'my-class';
    }
  }
}