To remove the System Settings submenu of the Applications menu, edit /etc/xdg/menus/applications.menu, by adding the following before the final </Menu> tag in the file:
|  ...
  <Menu>
    <Name>System Settings</Name>
    <Deleted/>
  </Menu>
</Menu> <!-- End Applications --> | 
The other submenus of the Applications can be removed in similar fashion. Note that the name of the submenus can be determined from the files located in the /usr/share/desktop-directories/ directory.