add class to dynamically loaded menu

Question 1

It's just a loading sequence issue. You jQuery fires when the DOM is ready, but probably before that nav is added since it's being added by javascript. If you moved that addition to the document ready function before you add the class, it should work. See this updated fiddle.

http://jsbin.com/urIlAlO/8/

I also moved all the logic from the head section to the body so it's non-blocking. Essentially, what I did was change your document ready function to below:

 $(function() {  
           var strGlobalNav='<ul><li><a href="//testonline/" alt="test Online Main Page">testOnline</a></li><li><a href="//testonline/ec/" alt="Employee Center Site">Employee Center</a><ul><li><a href="//testonline/ec" alt="Employee Center Site">Employee Center</a></li><li><a href="//testonline/ec/awards" alt="Awards &amp; Recognition Site">Awards &amp; Recognition</a></li><li><a href="//testonline/hr/benefits" alt="Benefits Site">Benefits</a></li><li><a href="//testonline/hr/EERelations/Pages/Default.aspx" alt="Employee Relations">Employee Relations</a></li><li><a href="//testonline/hr/Employment/Pages/Default.aspx" alt="Employment">Employment</a></li><li><a href="//testonline/ec/training" alt="test University Site">test University</a></li><li><a href="//testonline/ec/healthandsafety" alt="Health &amp; Safety Site">Health &amp; Safety</a></li><li><a href="//testonline/sites/offices" alt="Office Locations Site">Office Locations</a></li><li><a href="//testonline/ec/travel" alt="Travel Site">Travel</a></li><li><a href="//testonline/ec/tso" alt="Total Service Organization">TSO</a></li><li><a href="//testonline/ec/vidconf" alt="Video Conferencing Services">Video Conferencing</a></li></ul></li></ul>';
             $('#test-nav-wrapper').html(strGlobalNav);
            //clean up the row of the mega menu. add css class to each element on bottom row.
            //only if more than 7 elements. if more than 16, mm-3
            jQuery('#test-nav-wrapper ul li ul').each(function(ulindex, ulele){
                $total = jQuery(this).children('li').size();
                if ($total <= 7) {
                    jQuery(this).addClass('mm-1');
                }
                else {
                    $cols = Math.floor(($total) / 8) + 1;
                    $remainder = $total % $cols;
                    $rows = Math.ceil($total / $cols);
                    jQuery(this).addClass('mm-' + $cols + ' total-' + $total + ' rem-'+$remainder );

                    jQuery(this).children().each(function(liindex, liele){
                     //alert("total: "+$total+", remainder: "+ $mod+", ulindex: "+ulindex+", liindex: "+liindex);

                        jQuery(this).addClass('col-' + Math.floor((liindex / $total * $cols)+1) );
                        if( (liindex+1) % $rows == 0) {
                            jQuery(this).addClass('last');
                        }
                    });

                    for (var colcount = 1; colcount<= $cols; colcount++){
                        jQuery(this).children('.col-'+colcount).wrapAll('<div class="col" />');
                    }
                }
            });          


});

UPDATE: Just reread your question and noticed 'My menu is constructed by consuming web-service returned javascrip'.

Do your jquery stuff in the body afeer the JS generated by your web service. start your on ready function by adding the menu to the nav as below, before doing your check and adding the classes.

$(function() {
  $('#test-nav-wrapper').html(strGlobalNav);
  //clas checking stuff here
})

That should work just fine for you. It would also be nice to know how you're getting the menu from a web service. If it's a service on the same domain, consider using $.ajax() and then doing your check and adding the class in your success function. See http://api.jquery.com/jQuery.ajax/

Question 2

In your original code you missed "{" tag in jQuery(document).ready(function() this is why it's not working there!

       jQuery(document).ready(function()   
       {
        //clean up the row of the mega menu. add css class to each element on bottom row.
        //only if more than 7 elements. if more than 16, mm-3
        jQuery('#test-nav-wrapper ul li ul').each(function(ulindex, ulele){
            $total = jQuery(this).children('li').size();
            if ($total <= 7) {
                jQuery(this).addClass('mm-1');
            }
            else {
                $cols = Math.floor(($total) / 8) + 1;
                $remainder = $total % $cols;
                $rows = Math.ceil($total / $cols);
                jQuery(this).addClass('mm-' + $cols + ' total-' + $total + ' rem-'+$remainder );

                jQuery(this).children().each(function(liindex, liele){
                 //alert("total: "+$total+", remainder: "+ $mod+", ulindex: "+ulindex+", liindex: "+liindex);

                    jQuery(this).addClass('col-' + Math.floor((liindex / $total * $cols)+1) );
                    if( (liindex+1) % $rows == 0) {
                        jQuery(this).addClass('last');
                    }
                });

                for (var colcount = 1; colcount<= $cols; colcount++){
                    jQuery(this).children('.col-'+colcount).wrapAll('<div class="col" />');
                }
            }
        });

});

Fiddle