Government major = close
You're right in that trespassing laws vary from state to state - incidentally, these are closely related to stalking laws, as they are interlinked content-wise - but if the land is owned/leased/rented by a public university, the property (ex: Greek house) is still held in name by a person or organization implying continuing or temporary ownership. Therefore, a student who is kicked out of Greek housing and stays may be charged with trespassing if s/he continues to reside at that address.
Some states have an implied right of ownership that enforces trespassing as a state in which someone has invaded a private property or building without invitation. Others cases, such as land expanses, need posted proof that it is owned by someone else such as No Trespassing signs. But I'm pretty sure that you could be charged with home invasion, intent to burglerize or trespassing for being on a property without prior invitation - it all goes back to intent.
Sidenote: If you're looking in the windows of a structure on a property and you are on said property, you can still be considered a trespasser. However, you can always be charged with loitering if you insist on viewing the property on a public plot, seeing as how loitering laws are everywhere
Also, someone can call you in as a suspicious person and police can require you for questioning if someone reports you as a nuisance.