Sorting meta box values by start- and enddate and all dates in between

I think you can do the trick running 2 loops, in the first you prepare an helper array of posts ordered by date, in the second you display this array:

Something like this (completely untested):

if ( $agenda_query_full->have_posts() ) {
  $date_events = array(); // helper array
  $today = date('Y-m-d');
  while ( $agenda_query_full->have_posts() ) {
    $agenda_query_full->the_post();
    global $post;
    $metas = get_post_custom();
    // save event name in the post object
    $post->ename = array_pop( $metas['evenement-name'] ); 
    $meta_event_start = array_pop( $metas['evenement-datum-start'] );
    $meta_event_end = array_pop( $metas['evenement-datum-end'] );
    $dateRange = getDateRange( $meta_event_start, $meta_event_end ); 
    asort($dateRange);
    foreach ( $dateRange as $date ) {
      if( $date < $today ) continue; // skip past events
      if ( ! isset($date_events[$date]) ) $date_events[$date] = array();
      $date_events[$date][] = $post; // put post in helper array that is keyed by date
    }
  }
  if ( ! empty($date_events) ) {
    foreach ( $date_events as $date => $events ) {
      $datum = date( "d-m-Y", strtotime($date) );
      echo '<h3>' . $datum . '</h3>';
      echo '<ul>'; 
      foreach ( $events as $event ) {
        if( in_category( 'acties', $event ) ){
        echo '<li><a href="' . get_page_link( $event->ID ) . '">' . $event->ename . '</a></li>';
        } else {
        echo '<li>' . $event->ename . '</li>';
        };
      }
      echo '</ul>';
    }
  } else {
    echo 'No events found.';
  }
} else {
    echo 'No events found.';
}
wp_reset_postdata();