The episode is Family Guy Viewer Mail 1 from Season Three
That episode contains 3 different segments, and the second segment is called "Super Griffins", where the Griffins develop superhuman powers after being exposed to toxic waste from a tanker truck.
Peter Griffin has the ability to shapeshift (in that segment he transformed into a Tyrannosaurus Rex).
Lois Griffin becomes super strong, having superhuman strength.
Stewie Griffin's cranium doubles in size, having telekinesis.
Brian Griffin has the ability to move at superhuman speeds.
Chris Griffin has the ability to start fires by thought, developing pyrokinesis.
Meg Griffin has the ability to grow her fingernails longer or shorter on command.
Family Guy Viewer Mail #1 (Season 3|Episode 21)
-No Bones About It - A genie comes to Peter to grant him wishes; his last wish makes it so that he has no bones and must deal with life as a lump of lard.
-Supergriffins - The Griffins are exposed to nuclear waste and gain superpowers, which lead them to terrorize the city.
Peter got Morphing Abilities.
Lois got Super Strength.
Brian got Super Speed.
Chris got Pyrokinesis (ability to produce fire)
Stewie got Telekinesis (manipulative mind power)
Meg got the ability to grow her fingernails at will.
-Li'l Griffins - Tot-like versions of Peter and Quagmire try to out-brave each other in a haunted house to impress Lois in this little rascals parody.
well....i dont really know
iDate a Bad Boy
Meg.
Only in fiction and art. There never has been real griffins.
Jasper
Beer
They were exposed to toxic waste.
Boys Do Cry
iDate a Bad Boy
Mother Tucker
Bette Midler | The Rose
Brian griffins house of pain
From Method to Madness
Meg.
Dog Gone (US season 8/UK season 9)
Spikes of gold
Griffins are never referred to in the Bible .
Other griffins. There is no mythological ancestor in fable.