The most bizaree, screwed up comic in general, surprisingly, was not published in alt-weekly newspapers. It ran in a small number of mainstream daily newspapers in the mid-1980s. Move over, Bob the Angry Flower! Up yours, Maakies! Let Arnold through!
Arnold was by Kevin McCormick, and ran from January 3, 1983 to April of 1988. It was syndicated by Field Enterprise, which was bought out by Rupert Murdoch and renamed News America Syndicate, until it became North America Syndicate, which was bought out by King Features (the North America name is still used in some of the KFS comics). Phew!
The star of the strip was Arnold, a kid who constantly spouts random statements out of nowhere. His friend was Tommy, who is probably the only "normal" character the strip, and I mean that loosely. Their teacher was Mr. Lester. These three characters were the only ones to actually appear on-panel in the strip, until about few months before the strip ended, when Arnold gained a younger brother named Sid. Every other characters, including Arnold's parents (also equally weird), only spoke off-panel.
The strip is fairly well-known despite its short life in a small number of papers. Chances are, if you got the strip in your paper, you would've remembered it.
Kevin McCormick joined the staff of Paws Inc. (Garfield) after the strip ended, but eventually left cartooning behind. He's apparently running a school somewhere now.
You can see more strips here.