Really need advice regarding my Landlord not paying Property Tax

[Bibliofagus]

The tax sale happened on 6/17/14. I was never late on payments, so the eviction threats were shocking to hear from both of them. So you're basically saying I could be paying the previous landlord for 17 days and the new landlord for 13 days.

What you said in response to Chtulhu however - if true - would trump all this. Forget what I said. What I meant to say was: You need to pay the rent to whomever has the right to receive it.
Normally this would work out the way I described, but your situation seems more complicated.

I'm terrible with this kind of thing so I don't really know how I'd go about getting a partial refund for the property tax

It says there on the site I linked how you can apply.

and I'm not sure what you meant by possibly having a claim on my government's owner.

I said government/ex-owner and meant government or ex-owner.

The ex-owner part is mostly hypothetical. The thing is: Tax refunds can often be reclaimed several years back. At least this is the case in my country. But the tax in question was not paid at all for quite some time, so your government might say that there were no taxes paid to be reclaimed. Which would mean you have a claim on your ex-landlord.

Never mind about all that. All you need to know and do to maybe get some extra money is apply for the refund.