drupal_add_js and inline code
First of all you need to replace $ with jQuery and secondly you also need to put the width and coulmn properties inside double quotes. i.e, 

drupal_add_js('
jQuery(document).ready(function () {
    if (jQuery.browser.msie &amp;&amp; jQuery.browser.version &lt; 10) {
            jQuery("li#megamenu-mlid-774 .megamenu-items, li#megamenu-mlid-842 .megamenu-items").columnize({
                "width": "420",
                "columns": "3"
            });
        }
  });', 'inline');