The 3rd U.S. Circuit judges say the posts are protected under previous Supreme Court case law on student speech, because the parodies weren't likely to cause significant disruptions at school.
Monday's rulings have been highly awaited by school districts wrestling with how to handle student speech on the Internet.
Six judges dissented in one case, saying they feared online attacks on school officials would go unpunished.
The American Civil Liberties Union says districts infringe on student speech when they reach beyond school grounds.
Judge D. Michael Fisher, in the dissent, calls any distinction between off-campus and on-campus speech "artificial" in the age of Facebook, Twitter and smartphones.