To do the taxonomy query in your case, the code would be like this:
if (isset($_POST['cat']) && !empty($_POST['cat'])){
$args['tax_query'] = array(
array(
'taxonomy' => 'roadkill_category',
'field' => 'id', // or slug
'terms' => $_POST['cat'],
'operator' => 'IN'
)
);
}
If you have further questions about tax query, please refer to the Codex.