<?php
$letters = range( 'a','z' );
array_push( $letters, 'å', 'ä', 'ö' );
foreach ( $letters as $index=>$letter ) : ?>
<h3><?php echo $letter; ?></h3>
<ul>
<?php
$tags = get_tags( array('name__like' => $letter, 'hide_empty' => 0) );
foreach ( $tags as $tag ) :
?>
<li><a href="/tag/<?php echo $tag->slug; ?>/"><?php echo $tag->name; ?></a></li>
<?php endforeach; ?>
</ul>
<?php endforeach; ?>

function sort_nordic(&$array) {
  uasort($array, 'nordic_cmp');
}
function nordic_cmp($a, $b) {
  // If å, ä, and ö is missing from first string, just use PHP's native function
  if (preg_match('/([å]|[ä]|[ö]|[Å]|[Ä]|[Ö])/', $a) == 0) {
    return strcoll($a, $b);
  }
  // If å, ä, and ö is missing from second string, also use PHP's native function
  if (preg_match('/([å]|[ä]|[ö]|[Å]|[Ä]|[Ö])/', $b) == 0) {
    return strcoll($a, $b);
  }

  // Arriving here both the strings contains some characters we have too look out for
  // First, create arrays from the strings so we can easily loop over the characters
  // Comparison is made in lowercase
  $a_arr = preg_split('//u', mb_strtolower($a), -1, PREG_SPLIT_NO_EMPTY);
  $b_arr = preg_split('//u', mb_strtolower($b), -1, PREG_SPLIT_NO_EMPTY);

  // Get the length of the shortest string
  $end = min(mb_strlen($a), mb_strlen($b));

  // Loop over the characters and compare them in pairs
  for ($i = 0; $i < $end; $i++) {
    // Check if character in the first string is one that we have to correct for
    if (mb_stripos("åäö", $a_arr[$i]) !== false) {
      // Computes the corrected return value. The first character "-" is just a
      // nonsene placeholder to return 1 for "ä", 2 for "å" and 3 for "ö"
      $r = mb_stripos("-åäö", $a_arr[$i]) - mb_stripos("-åäö", $b_arr[$i]);
      if ($r != 0) {
        return $r;
      }
    } else {
      // If the character is not a character that we have to correct for
      // the PHP native works fine
      $r = strcoll($a_arr[$i], $b_arr[$i]);
      if ($r != 0) {
        return $r;
      }
    }
  }
  // Fallback: If so far there has been no call to return() then the
  // strings are idenical up until the length of the shorter string.
  // Then let the lengths of the strings determine the order
  return mb_strlen($a) - mb_strlen($b);
}