His team needed to explain to him omnivorous didn't mean "omnivorous like a forest fire".
Another character later defined him as a "Mundivore" (latin for world eater).
To clarify, when Schlock accidentally ate something infected with military immortality nanobots he spat it out before a conclusion was reached, but his digestion seemed to be winning. On another occasion, he ate tissues that tried to plate his insides with aluminum, and just considered the process tingly. He has even stated that he likes the tingly process of eating hostile nanotech, on the grounds that "food that fights back builds character".
Not from the comic itself, but Brian Clevinger (author of 8-Bit Theater) regularly makes his newsposts the latest episode of What Did Charlie Eat, starring his Extreme Omnivore cat. At the time of writing, the latest update was "iPhone earplugs".
Moloch von Zinzer probably also qualifies, at least when it comes tobeverages. His taste in drinks and associated iron stomach is actually something of a running joke among the fanbase, leading to, among other things, him being pegged as 'most likely to accidently Jaegerize himself'.
The Wayward Vagabond will eat anything, as long as it's green (or has been green at some point in time). This includes a pumpkin, a potted plant, several pieces of chalk, and a chunk of uranium.
He also learns proper human etiquette by eating a book on it (though to be fair, he reads each page before eating it).
Terezi is a synesthete who smells and tastes colors. Her favorite flavor is bright red. This apparently extends to chalk.
Weesh, of the eponymous comic Weesh, who isn't human.
Weesh: Mm. This blue mayonnaise you've got is delicious. Boy: Blue mayo? ...That's dishwasher soap. Weesh: Ah. I wondered why it was under the sink.
Warp-Aci will "eat" anything smaller than them... which becomes a real problem if they grow. It helps that they have no actual digestive system — anything they 'eat' is simply teleported somewhere random.
Also, Abel once ate a pillow. In his defense, he was having a dream about giant marshmallows.
Tanked from Bear Nuts. Constantly in such an altered state, he'll (at least try) to eat anything he can fit in his mouth.
In Freefall Sam Starfall is apparently pretty tough in this department. Probably makes up for his general weakness in nearly every other one.
As long as it's metal, Rusty will want to eat it. At least he (usually) asks first...
Gelatinous Cube will eat anything organic. The bones just take a little longer.
Llewellyn in Ozy and Millie, being a dragon, has been known to drink gasoline and lighter fluid, and once claimed to have eaten Joe McCarthy's car. While Aunt Tulip ate an entire bus at the family reunion.
Bloody Urban gives us Shannon, whose current canon toll includes sheep, human hearts, corpses, a pizza covered in corpse parts, a whole vending machine full of candy, an Apple iPad and one of his childhood classmates.
In tinyraygun, there's Doppler, a newly hatched alien that responds to having a gun pointed at it by snatching it with its tongue and crunching it down.