In a game of diplomacy I am playing, a Turkish army in Moscow is attacking Warsaw with support from Ukraine, Galicia, and Silesia. A Russian Army in Warsaw is attacking Moscow with support from Livonia and St. Petersburg. Finally, A Russian Army in Prussia is attempting to move into Warsaw. What happens?
Moscow is moving to Warsaw with strength 4 (itself + 3 supports). Warsaw is moving to Moscow with strength 3 (itself + 2 support). The Army in Prussia moving into Warsaw is irrelevant (It's of strength 1, which is also less than 4). The MOS-WAR move has greater strength, so succeeds and the Army in Warsaw is dislodged. The Prussian army remains in Prussia.
In general, if you ever want to adjudicate a situation in diplomacy, there is an online adjudicator at http://stabbeurfou.org/Interrogation.php that you can use.