Filter Select results based on selection

Seeing as my comments seemed to answer the question:

To get access to the URL params you want $wp_query->query_vars['myvar']: http://wordpress.org/support/topic/how-to-pass-value-in-wordpress-url, e.g.:

<?php
global $wp_query; 
$node_id = 0;
$args = array(
    'post_type' => 'jobs',
    'category_name' => $wp_query->query_vars['position_name']
);

$the_query = new WP_Query( $args );

The other parts of the question aren’t really WordPress issues, so Stack Overflow is the best place to ask them. For the updating the page you can either redirect the page onto itself using a javascript redirect for the onchange event or you can use AJAX to update the contents for the onchange event without a page refresh.