When someone is either so drunk or so sick that they both vomit and diarrhea at the same time. The resulting act dictates a person trying to decide to either vomit in the toilet and shit on the floor or shit in the toilet and vomit on the floor. Either way, the person is screaming and must support themselves with both arms, thus the Screaming Eagle has been performed.
A sexual act that involves a man having intercourse with a girl doggy style, and right before he climaxes he grabs both the girl's arms and holds them behind her back and he inserts his penis forcefully into her anus, and releasing her arms. This makes the girl scream and flap her arms like an eagle.
Guy 1: Sh*t its the cops get rid of that l
Guy 2: what should I do? Toss it?
Guy 1: no thats too obvious, he'll see it. You'll need to perform a screaming eagle.