First, please use wp_enqueue_script()
to add JavaScript to your WordPress pages. Also note that jQuery is loaded by default in WordPress; there’s no need for you to do it.
From that same page:
The jQuery library included with WordPress is set to the noConflict() mode (see wp-includes/js/jquery/jquery.js). This is to prevent compatibility problems with other JavaScript libraries that WordPress can link.
In the noConflict() mode, the global $ shortcut for jQuery is not available[…]
However, if you really like the short $ instead of jQuery, you can use the following wrapper around your code:
jQuery(document).ready(function($) {
// Inside of this function, $() will work as an alias for jQuery()
// and other libraries also using $ will not be accessible under this shortcut
});
[src]
So change your code to this:
jQuery(document).ready(function($) {
$('.one_fourth_style_4').stickySidebar();
});
and it should work with WP’s jQuery library.