Got it in the for loop for the invoice items, get the order_id and then the field values from that order:
$db = & JFactory::getDBO();
$query = "SELECT order_id FROM #__inv_orders_invoice WHERE invoice_item_id = $invoice_item->id AND invoice_id = $invoice->id";
$db->setQuery($query);
$order_id = $db->loadResult();
// get field values
$the_service = get_form_field_value($order_id, "service");
etc...