Is a Jew permitted to sleep in a room/house where there are idolatrous images on the walls, such as JC, etc.? What about non-Jews?
Before getting into the technical halachic aspect if it is permitted or not, it is surely not advisable to stay there when you are prone to looking at idolatrous images on a constant basis. These things can have an effect on us, and therefore it is best to try to correct the situation or find somewhere else to sleep. Having said that, it is not halachically forbidden to sleep in the room, however you should preferably not daven in that room, and if you have no choice at least it should not be facing the avoda zara. Additionally you should be careful not to bend down to pick something up in front of it, as it will look like you are bowing down to it.
Sources: Shulchan Aruch O:CH 94-8, M:B 29-30, Chayei Adam 23-5
Images/statues of people are not A"Z by itself, no matter what. You can have pictures of Rabbis and Moses and your grandfathers in your house.
What makes it A"Z is the fact that those are worshipped by different ways of worshipping an A"Z like in a church:
In a place where those pictures serve only as decoration, staying is permitted. Think about St. X hospital - lots of images that are not worshipped. My Grandma Z"l at 105 stayed in St. Louis hospital in Jerusalem for the last month of her life and it has a couple of statues inside.
In a place where those particular images are worshipped, it is forbidden to stay or visit (unless in a big need).
There's always a consideration of מראית עין - in any way don't let people think you're enjoying your stay.