According to
http://onw.innosked.com/?show=MAP , I don't see a WAW-STR flight on any carrier. You could do WAW-TXL-STR on airberlin, which seems to be the only 2-flight option. Since it's not that far, it's probably cheapest with Avios.
Avios? I don't have BA Avios only AA miles. Is there a way to convert those to avios? Which airline will have the least taxes between AY and AB?