Firstly, each card belongs to one ,or sometimes more, of the six great houses, unless it is neturtal. Can decks only be built using cards of the house you are playing and neutral cards? Or is it only cards with the text "House X only" that are restricted this way?

Also, when playing, can only one player play each house at a time, or is a game, for example, with 3 house Lannisters and 1 Baratheon possible? The drawback to that being, as I imagine, only that 3 players would share a number of unique cards and therefore limit one anothers options?

1) Only restriction that cannot be bypassed is the "House X only" othervice you can play cards from other houses than what your own House card is, but - when you play a card that doesn't have the same house affiliation as your house card you have to pay a gold penalty of 2. So it gets very expensive to play out of house cards as they cost two more to play. Neutral cards don't have gold penalty and they can be played by any house normally.

2) You are probably talking the 4 player format "melee" here? There is nothing to limit on how many houses are used, it is even possible that everyone in the table is playing the same house. If your playgroup only has 1 coreset this will most likely not happen as there are not enough cards to make multiple decks for the same house.

The drawback to that being, as I imagine, only that 3 players would share a number of unique cards and therefore limit one anothers options?

Also note that even if playing 3-4 player melee and everybody is playing the same house, each person can have the same unique card out. Every one of you could have the same Stannis out for example...