Make this simple.
Presuming that the terms & conditions of your booking or a specific revision permitting refunds, e.g. "Covid-19 policy" exists, that you have requested a refund, and that a reasonable time period has passed and you have neither a refund nor that one has been approved, you should immediately initiate a chargeback. Presuming that you can upload supporting documents, I would provide a copy of the original reservation, the cancellation request, and the provisions you rely on for a refund, e.g. t&c and Covid-19.
DOT, which regulates air carriers not hotels or TA's, defines "reasonable" as 7 days. As there is no defined period for Orbitz, I would give it the 7 days and proceed on the 8th day.
If your refunds come through while the chargeback is pending, you can always withdraw it.
But, there is no reason to spend time or effort chasing the third-party vendor, in this case, Orbitz.