"Please leave the room in order" is definitely correct, as is, "Please keep the room in order." Both "leave" and "keep" are verbs in this sense, but they would have slightly different connotations in this context.
Leave could mean, "allow to remain", as in, "Leave my coffee alone!", but in context, it will be obvious that you mean it in the sense of to "go away from"; the implication is, "When you leave, make sure the room is in order." (Yes, I know that you'll be making messes in the kitchen/coffee room, etc., but clean up before you go.)
Keep, on the other hand, would be used in the sense of, "continue or cause to continue in a specified condition, position, course, etc." (What you're saying is, "Look here, this is an office, there's no reason to be rearranging furniture to dance on break, KEEP THE ROOM IN ORDER!)
Note: definitions taken from Google Search's primary result for, "[whatever word] definition".
Edit: as Hotlicks points out in comment above, "in order" may not be the best choice of words to convey your intended meaning. Tidy, neat, clean, shipshape, or all of the above might serve you better; or you can just hire a janitor and forget about the sign.