ASC and DESC separately from orderby

I would do something like this:

<script type="text/javascript">
    //http://www.netlobo.com/url_query_string_javascript.html
    function gup( name, default_value )
    {
      name = name.replace(/[\[]/,"\\\[").replace(/[\]]/,"\\\]");
      var regexS = "[\\?&]"+name+"=([^&#]*)";
      var regex = new RegExp( regexS );
      var results = regex.exec( window.location.href );
      if( results == null )
        return default_value;
      else
        return results[1];
    }   
    //here you can output default values for sortby and order by your php script
    var orderby = gup("orderby","");
    var order = gup("order","");
    function change_url() {
        var url = "<?php echo $short_page_url; ?>?orderby="+orderby+"&order="+order;
        document.location = url;
    }

    //you still have to let javascript or php select the correct options
</script>
<div class="sort">
   Sort by  
     <select onclick="if (this.value) { orderby = this.value; change_url(); }">  
        <option value="" selected="selected">Latest first</option>  
        <option value="date">Oldest first</option>  
        <option value="title">Titles A-Z</option>  
     </select>
   Order 
     <select onclick="if (this.value) { order = this.value; change_url(); }">  
        <option value="asc">asc</option>  
        <option value="desc">desc</option>  
     </select>
</div>