So basically from what you're saying: I should invite people to the apartment, then check the upper bar in the casino then check back at the apartment to get all squad dialogue?
Okay, here's what you do:
1) To get special squadmate interaction such as meeting up with them and stuff, special conditions must be met while others you just gotta keep waiting. Take Jacob and Samara for example, if you have met them, or if you haven't this isn't much of a spoiler anyways. They'll be waiting at the Citadel for you, and until you talk to them, you will not unlock any special interaction with them within the Citadel DLC. It can be a little impatient to just wait, but that is to ensure that you do not do everything all at once. Completing side missions and side quests along with story progression after the Citadel DLC arc will unlock things along the way.
2) Inviting to PARTY: The invitations are held within the very right icon within your apartment's message terminal. You can only invite individuals that you have met and are still alive. There is an "Invite All" option, and so, watch out for that one. To actually get this option within your apartment's message terminal, you have to head up back to the Casino bar to purchase "Party Supplies". After this, the option to invite squadmates will be possible, but take note that Cortez, EDI, Joker, James, Liara, and Traynor are automatically invited which is pretty stupid, but they're forced onto you because any other squadmate that isn't already auto-invited are squadmates that can potentially die in the previous games.