I would always use "living room". "Parlour" sounds very old-fashioned, and you're unlikely to see it unless you're reading novels written in the early 1900s. I've never heard of a "sitting room" or a "drawing room"; but, according to Google, a "sitting room" is just the British word for a "living room". I found this website explaining the difference between a drawing room and a living room: http://www.homedit.com/difference-between-living-room-and-drawing-room/ According to the above website, a drawing room is very similar to a living room, except its sole purpose is to receive guests (whereas a living room can do this, as well as be used for recreation). In the house we grew up in, we had two living rooms. One had a TV and a ping pong table and we used it all the time. The other was really only used when we had people over. According to the above website, the latter room was actually a drawing room.

The typical modern house has a "living room" for the family to congregate in and to receive guests. This is also called a "sitting room", but I think that name is a little old-fashioned or regional. In a older, grander house, the living room would be where the family would gather, but not where they would receive guests. That would be either the parlour or the drawing room. If a house ran to both, then the parlour would be where you met a drop-in visitor for coffee or tea during the day, whereas the drawing room would be for larger gatherings exceeding the capacity of the parlour, or specifically for the purpose of withdrawing to after a dinner party (the ladies traditionally doing so first, then being joined by the gentlemen after their manly lingering at the dinner table).