From my reading of the manual, fleets use upkeep only if the move/attack and don't end in port. This means that port-to-port transfers are free. However, my big American stack in port says x oil use, where x is the number of ships. From the manual tables, DDs cost 2, CA 2, BB/C 4, CV(L) 3. What is this discrepancy?
Fleets in port, HQs (except for the Chinese), and multiples of land units do require oil upkeep interturn, but it's less than movement/combat would require. The details on how much are in the manual.