Remove your ajax call first and simply place the html inside orders like
$(function () {
var name = $('#<%= name1.ClientID %>').val();
var drink = $('#<%= drink1.ClientID %>').val();
$('#<%= add_order.ClientID %>').on('click', function () {
var items="<li>name: " + name+ ", drink: " + drink+ "</li>";
$('.orders').html(items);
});
});
Hope this helps