Hog packing houses have prided themselves about using almost all of the animal—“everything but the oink.” The phrase “everything but the squeal” dates to about the 1860s. “Everything but the oink”—a newer variation of the same phrase—is cited in print from 1961.
       
 
18 October 1961, Daily Capital News (Jefferson City, MO) pg. 3, col. 5:
And, like the meatpackers who find uses for everything in the pig except the oink, the walnut processors make the most of the side products. 
 
23 December 1968, Fresno (CA) Bee, pg. 16A, col. 1:
“My uncle is a drinker who prides himself on getting away with saying anything that comes into his head to anybody. Speaking of me last night, he suggested my husband ‘boil her down and use up everything but her oink.’ Isn’t that the worst insult you’ve ever heard?”   

6 November 1971, Dallas (TX) Morning News , section D, pg. 2:
So marvelous an animal is the pig that it’s purported to be possible to use every part of the beast but the “oink,” and now modern food processors have apparently found a use for even that.       

6 July 1974, Dallas (TX) Morning News, section B, pg. 7:
Lion Country Safari in Irvine, Calif. has topped (or maybe bottomed) the old gag about pig farmers being able to sell everything except the oink.
 
Google Books
The World Encyclopedia of Food
By L. Patrick Coyle
Published by Facts on File
1982
Pg. 394:
Though not as popular, hogs may be the most efficient meat source, because, as the saying goes, meat packers use “everything but the oink.”
 
28 May 1989, Los Angeles (CA) Times, “Ray Charles Keeps On Keepin’ On At Age 58” by lawrence Christon, Calendar section, pg. 3:
...(in describing how they feasted on pig, he recalls, “We ate everything except the oink”).
 
Google Books
Food: a dictionary of literal and nonliteral terms
By Robert Allen Palmatier
Published by Greenwood Publishing Group
2000
Pg. 121:
EVERYTHING BUT THE OINK Every part of the pig except the squeal. Source: PIG. The pig has been the domesticated animal of choice for settlers in North America since the 16th cent., and it remains the favorite source of meat and meat products in the American South. At one time or another almost every part of the pig has been put to good use as food for humans: the belly, the feet, the hams, the hocks, the intestines, the jowls, the knuckles, the loins, the shoulders, and the sides. SOmetimes an entire pig (minus the head, feet, tail, and internal organs) is roasted on a spit in a large gas-fired barbecue oven; and in Hawai’i, on special occasions, an entire pig (including the head, feet, and tail but excluding the internal organs) is barbecued over coals in a pit dug in the ground. In the 1990s a company named Oink-Oink, Inc., was founded in Detroit, Mich., to produce treats for dogs from the various parts of pigs, such as the heart, hooves, liver, and snout, as well as the original product: roasted pig ears. The company’s slogan is “Everything But The Oink.”
 
Google Books
Everything But the Oink:
The Significance of the Swine in Pennsylvania Dutch Culture.
By Sime Bertolet
Published by University of Texas at Arlington
2004
 
Google Books
Extreme Cuisine: The Weird & Wonderful Foods that People Eat
By Jerry Hopkins and Anthony Bourdain
Photographs by Michael Freeman
Published by Tuttle Publishing
2004
Pg. 86:
Our guide then said something that I remember to this day: “Every part of the pig is used, everything except the oink.”