DCs
The "why" is easy. They were no longer effective against the likely targets. The speed and diving capability of submarines had improved but there isn't much you can do about the performance of a conventional DC. It still sinks at the same rate and its lethal radius is still subject to the inverse square law. The new weapons in the inventory were much more effective, Mk44/46 so the least effective item can be dropped. The only area where the conventional DC might have been tactically useful was in shallow water (>100 fathoms). Not really the sort of area a submarine would wish to operate unless absolutely necessary. But if you were prosecuting a contact in that sort of area an MPA is probably not the ideal platform anyway.
The "when" bit I am not sure about. The conventional DC had certainly gone from the inventory by the mid 70s. It may have been listed as an option when the Nimrod came into service, but I very much doubt that any were ever released by squadron crews. If they were ever dropped it would only have been on the initial weapon release trials.
The Nuclear Depth Bomb (NDB) on the other hand remained in the inventory until approx. 1992.
YS