In the context of air hockey, specifically a well-worn game of air hockey that may be found in a local tavern, a "dirty bird" happens when your opposing team scores three goals in quick succession in a row. The use of the term "dirty bird" would be especially appropriate when the team happens to score three goals through a small-but-exploitable gap in the left side of the goalie net. The term "dirty bird" is said gruffly, never sweetly.
In fact, if you know someone who complains a lot under their breath, partly hoping to be heard and not be heard, then that is the voice you can use when you say "dirty bird."
You can also say something is a "dirty bird" whenever something less than desirable happens.
Example 1
Person 1: Hey, you just scored three goals very quickly in a row using similar techniques that exploit a gap in my goalie!
Person 2: I did. That's called skill.
Person 1: (Mutteringly) That's a dirty bird.
Example 2
Person 1: I ordered a sandwich, but they gave me soup instead.
Person 2: Oooh, that's a dirty bird.
When you put your finger in your own or someone else's butt hole and flip someone off
What is left of a football team after being decimated by the Atlanta Falcons.
The Green Bay Packers were a good football team until they played the Atlanta Falcons in the 2016 NFC championship game, now they are just dirty bird fodder.