Actually, it's pretty easy to understand why the aircrews nickname the aircraft like this, the F16 is an exceedingly agile aircraft - it can sustain flat 360 degree turns at 450 knots. There are very few aircraft around the world that can do this.
The F15's nickname is also easy to understand - Rhodan was a very large bird in the Godzilla movies and the F15 is one of the largest fighters around.
The F14's nickname might be harder to understand, but when you know that a Tomcat has barely enough thrust to make it off the carrier deck with a full combat load it becomes a lot clearer.
(In all fairness, I haven't seen a Navy crew call an F14 a "turkey" yet - I think it's mostly an Air Farce term)