We want to report on several status combinations like each order that has status 'Not deleted' and 'Not technically completed'. What set up is required?

Check transaction CO28. In the selection screen note the possible selection 'System Status' . You can select TECO for technically complete an DLT for deleted from the list. Select the Excl. indicator also.
You may also try transaction CO26 (Logistics -> Production -> Production control -> Control -> Information systems -> Order Info System -> Object overview). Before executing the transaction report, combinations of statuses can be selected or exclude them.