We need more context. It says the lavatories “also” had a birthday so there must be a mention of something else before.

It's certainly unusual to talk rooms having birthdays. I can't even guess what that's supposed to mean since it's not clear at all. But "unlocked" is easy to define. It's the opposite of locked. He didn't lock the door. Putting newspaper on a nail seems to indicating that they use old newspaper as a substitute for toilet paper.

Where did you find this sentence? I am a native English speaker and do not understand the sentence myself. The words in the sentence don't make sense- for example, a lavatory is another word for bathroom, and rooms cannot have birthdays. Good luck on your language learning! I'm sorry you encountered such a weird sentence.