Ok I know that the 24 man at least happens before the msq as I had done the msq before starting the 24 man and both Yugiri and Tataru still do the whole sorry we can't help you speaches. Which makes sense if this happens before the msq because the wall wouldn't be up and during the quest line it's mentioned that the Dalmascan groups were scattered and kind of in fighting. While if you go and do the msq first there's a Dalmascan rep there in the room when you go see Hien.

The 24 man also at least happenes before or after the four lords as I highly doubt Tataru would leave her watching of Koryu and the other three lords to go meet us at Hancok's. I feel like this is one of the rare times things aren't running parallel to the point it doesn't matter when you finish which.