For each expansion you have:
1) If you don't enable it in the lobby, it has no impact on whether they can play with you or it being in trial mode.
2) If you enable it in the lobby, but they don't have it installed, then they can't play in that game (they just don't have the images, etc).
3) If you enable it in the lobby, and they have it installed, but they haven't entered a license key for it (it's still in trial mode, in other words), then they can play in that game but it will be a trial-mode game (campaign stops at 3 hours, etc).
4) If you enable it in the lobby, and they have it installed, and they've entered a license key for it, then they can play and it will be a normal (non-trial) game