The socket is a combined headphone and microphone jack, so may require a four ring connector or some other proprietory adapter plug to work.
It could just be a faulty connector, but unlikely. The fact that the audio continues to come from the speakers suggests that whatever you have plugged in so far is not going in far enough to disconnect the speakers. This function is usually performed by one of the connectors in the socket being pushed apart and opening a switch breaking the circuit to the speakers and feeding the audio to the headphones instead. Possibly the rings on the headphones you have tried have the wrong ring spacing and are bridging the circuit to the speakers instead of breaking it.