Tear out basement bathroom (improper install and not operable) and cap off sewer line to reduce odor. 

It had been on the MLS for several months, was really ugly, and had terrible pet odors.

The only way to prevent that is to really screen your tenant to ensure they've been problem-free with previous Landlords while owning the cat and by conducting regular inspections to verify the tenant is cleaning the litter box regularly and preventing any odors.

Carpet is cheap and refinishing hardwood is messy and has a lingering odor for a while. 

https://www.odorfreemachines.com/cigarette-odor-removal/

As an SFR that concern may apply to neighbors if smoking outdoors or it may effect the odor of your house if smoking indoors.

Is the girlfriend still going to be responsible for her cats odor and carpet clawing?

According to the Airbnb guest, the cigarette odor permeated every part of the building, including the foyer/common areas and the Airbnb unit.My Airbnb guests left me a scathing 2 star review, with one star for value and cleanliness due to the odor.

Make sure you solve the odor problem before you put new flooring down or you will continue to have the smell.

There doesn't seem to be any real, demonstrable foul here so ... onward and upward!