How do I put an ‘if clause’ in an SQL string?

For your specific query, you can do:

UPDATE purchaseOrder
    SET purchaseOrder_status="COMPLETED"
    WHERE purchaseOrder_ID = '@purchaseOrder_ID' and
          not exists (SELECT *
                      FROM itemsOrdered WHERE purchaseOrder_ID = '@purchaseOrdered_ID' AND status="PENDING"
                     )

However, I might guess that you are looping at a higher level. To set all such values, try this:

UPDATE purchaseOrder
    SET purchaseOrder_status="COMPLETED"
    WHERE not exists (SELECT 1
                      FROM itemsOrdered
                      WHERE itemsOrdered.purchaseOrder_ID = purchaseOrder.purchaseOrdered_ID AND
                            status="PENDING"
                      limit 1
                     )