Columbia is a fairly liberal school, so strictness is not very. . .strict. The feeling around campus is that Columbia encourages you to be yourself, but not to cause discomfort to others.
In the classroom, each professor will set the tone for his or her own classroom. Respect is a must. On campus, Columbia suffers from some vandalism, but other than that, there aren't too many problems with behavior. In the dorms, this is where strictness is actually enforced. Nothing extreme, but if you are doing something they told you not to do (like smoking weed), you'll get busted.