Fixing issues on testing server

:-)
You have a lot of custom files there.
The custom.css, the woocommerce-mod.css and they seem intermixed in a compressed file. There is no @media instructions for small or big screens.

This is what the browsers sees after mixing all the custom and modded code:
<style type=’text/css’ media=’screen’>
#top #header_main > .container, #top #header_main > .container .main_menu .av-main-nav > li > a, #top #header_main #menu-item-shop .cart_dropdown_link{ height:150px; line-height: 150px; }
.html_top_nav_header .av-logo-container{ height:150px; }
.html_header_top.html_header_sticky #top #wrap_all #main{ padding-top:180px; }
</style>

And instead of going to Enfold CSS to handle the Hamburger menu, it goes to your woocommerce mod css:
.html_visible_cart .av-burger-menu-main {
padding-right: 25px;
}

It is not seeing the enfold css which makes the Menu act responsive.

I think the Menu issue started after someone tried to make the woocommerce shopping cart act pretty.
Just my 2 cents.

Sometimes it takes time to see the change, deleting the cache and deactivating the optimize (minified) css funtion helps.

I am not seeing woocommerce now at all. This theme should work well with woocommerce. Maybe you should open a new ticket.
I have a future project with woocommerce on one of my sites that runs Enfold.