Among some of the more outrageous cartoon characters, Screwy's feats include pulling objects out of thin air, doubling himself, and breaking the fourth wall, all the while uttering a characteristic cackling laugh.

The character was not as successful as Avery's Droopy was at this time, appearing in only five cartoons: Screwball Squirrel (1944), Happy-Go-Nutty (1944), Big Heel-Watha (1944), The Screwy Truant (1945), and Lonesome Lenny (1946).

[2] Most of his cartoons had him paired with Meathead Dog (voiced by screenwriter Cal Howard in Screwball Squirrel, Tex Avery in Happy-Go-Nutty, and Pinto Colvig in The Screwy Truant) as his adversary.

The 1946 cartoon begins with a wealthy woman purchasing the squirrel at a pet shop with the intention of giving him to her large dog Lenny as a companion.

After casually squeezing and pulverizing a big chew bone with his paw and crumpling his metal food bowl, he sits up, turns to the audience, and says, "You know, I had a little friend once, but he don't move no more."

In that cartoon, however, as a dead Bugs Bunny is being carried away by a guilt-ridden Elmer Fudd, the rabbit awakes to speak to the audience about the opera parody's sad ending.

In 1993, Hanna-Barbera resurrected Screwy in new animation for the series Droopy, Master Detective as part of Fox Kids' programming block of Saturday morning cartoons.

In 2013, both Meathead and Screwy Squirrel made appearances as residents of "Fairy Land" in Tom and Jerry's Giant Adventure, retaining most of their traits.

Several Screwy Squirrel cartoons were released as bonus features on classic Warner Bros. titles including: In March 2020, Screwball Squirrel, The Screwy Traunt, Big Heel-Watha and Lonesome Lenny were released on Blu-Ray, fully restored and uncut, by Warner Archive as part of Tex Avery Screwball Classics: Volume 1.