Is this an invasion of privacy/against the law?

[Yeti]

It would mainly be against the law if they had to hack into your Facebook account to read things.

It sounds like they're simply reading what you've publicly posted. That's not against the law. Though you may technically be paying them rent, for better or worse, relatives are also going to get a bit more nosy at times, and most would say it's reasonable for them to have some concern about you. If you don't want your "landlords" nosing into your business, you can move to a more formal rental, and you can restrict what you post publicly on Facebook.