I am to figure out something, and can't find any reference. I wonder: does it make sense to talk of a delta or other greek of a strategy? It seems that you can't put a price exactly on a call spread for example, so would that mean that delta metrics for a call spread would be simply the deltas for each option of the call spread?
If you have two or more options (or other derivatives) with the same common underlying, then you can add their deltas and most other greeks (but not e.g. moneyness). But if the legs have different underlyings, then netting their risks may lose important details.
Having said that, risk reports showing total interest rate delta across all currencies and tenors, or exchange rate delta across all currencies are quite common in practice.
Related question: Aggregate Greeks calculations