Contact a local odor removal service and have them come over to analyze and recommend the best method for remediation.

On the other hand, I've heard of an investor that got roped into a project that was half done, with no permits.... they hung tarps in front of the windows and pulled long shifts, including getting an electrician to come work in the middle of the night... and got it done.... no harm no foul.  

You are responsible for the safety and health issues in your building, and hoarding and odors like you describe are health issues (think rats) for the entire building. 

I guess if the offer is not accepted, no harm no foul.

I'd like to avoid anything that would make it unpleasant to live there (odors, damage) whereas we're fine with "preference" items like countertops, flooring, paint. 

If there were no victims, there would be no harm, no foul.

The other unit smells heavily of Kilz spray which has been used to cover up previous pet odors, but I'm hoping this can be ventilated.About the owner: He is 74 yrs old, wanting to retire...

We have been sick since we moved in the apt upstairs and we told you there was mold in the stairway where the airconditioner unit is... we smelled a musty odor in the stairway and thought it may have been the rug and asked if we could remove the rug.

They will likely cry foul on that approach.

@Mark Ferguson  Nice years work... congrats.... put the jetsmarter app on your phone. you earned it. then drive the lambo up to the air-stairs those always make great photos of success  :)I think this will be my best year ever in Real Estate as for once all the cylinders were hitting and I only had one fouled plug.. a project on the Oregon coast were I lost 30k..