Main 4 inch waste pipe broken
Let me preface this with a disclaimer; I am not a lawyer nor a health professional.

That said, the smell is likely hydrogen sulfide which in high enough concentrations can kill you, but since the problem is fixed it probably isn't nearly strong enough for that; most likely you'd just experience respiratory irritation. I recommend trying to keep it aired out as much as possible, so the gas doesn't build up. You should contact your landlord and get them to address the issue.

As far as your rights, that is entirely dependent on your location. If your landlord won't address the issue, this is probably the point where you should get your local health department involved; in most jurisdictions they can force property owners to address issues that are public health concerns.