Closing WP_LINK_PAGES DIV ID w/After Argmuent

First, declare the after arg at the beginning of your code:

$args['before'] = '<div id="link_wrap">';    
$args['after']  = '</div>';

When there is a next page, the arg is overwritten, so you’ll have to add the closing tag at the end:

if ($page<$numpages) # there is a next page
    $args['after'] = ' '. _wp_link_page($page+1)
       . $args['link_before'] . $args['nextpagelink']  . '</a></div>'
    ;