In Norway King Harald has a few "state" jobs; he has to sign all the laws passed by the Parliament and he also have the right to veto any law two or three times before it is passed anyway, but he never do that, he also holds the Government meeting in the Palace every Friday with all the ministers (secretaries of state and departments) and he also opens the Parliament every autumn, giving a "state of the nation" speach. If the King is indisposed to do these things, the Crown Prince will be his "locum".
I also believe the royal family have an important "public relations" function, representing Norway in the world. So I feel that their function is not obsolete.
And yes, the King and Queen live in the Palace in Oslo, the Palace is owned by the Norwegian state, as well as other manors and villas they use when they are visiting other parts of the country. The Crown Prince and his family live at Skaugum, but I'm not sure if that manor is privately own by them, or if it also belong to the Norwegian state.
In Norway there is very little pomp and circumstance, compared to other monarchies such as Sweden and Denmark. It's not the Norwegian way, but here is a certain feel of ceremony at gallas and such, and when the royal family is visting the other parts of Norway, opening buildings etc. The lack of pomp and circumstance may be seen in connection to the fact that Norway does not have any nobility, and both Sweden and Denmark does.