"What in the world is this song about?"
That's just about everyone's first reaction to "Paranoid Android." How could it mean anything? The lyrics seem disconnected, having no structural continuity or logical flow. Where you might have wanted to be able to construct a story out of the words, "Paranoid Android" is not a coherent narrative. While Radiohead songwriter Thom Yorke has said that the song was inspired by a bar incident, whatever narrative there is in the resulting lyrics isn't entirely self-evident—even at their clearest, the lyrics suggest little more than narrative fragments.
Lacking narrative, the song could only be though of as coherent in terms of its thematic focus. This kind of writing only started to develop significantly in the late nineteenth and early twentieth centuries, with the experimental poets of Modernism, and it's a style that Radiohead almost always uses in their lyrics.
To get a sense of what being "thematically coherent" means, consider some lyrics from "Let Down," another track from OK Computer:
Transport, motorways and tramlines, starting and then stopping Taking off and landing, the emptiest of feelings, disappointed people Clinging onto bottles, when it comes it's so so
Only a little analysis is necessary: the terseness of each phrase (which are often not even phrases) suggests emptiness. There's little need to editorialize, or perhaps, little that means anything in the first place. The only emotion is the lack of emotion. Every phrase can suggest things on its own. And this lack of need for a full story means that the brusque first verse of "Let Down" still manages to evoke a sense of frustration with the modern transport system and with the way it controls our lives.
"Paranoid Android" does much the same thing, though the varied musical styles of the song might make it less clear. Some larger themes of the song include insanity, violence, and the rejection of the consumer lifestyle that characterized the '80s and '90s, and that continues to characterize the West today. Additionally, several distinct moods—paranoia, violent anger, and the desire for salvation—define the different voices of the song. But what's perhaps most important about the lyrics is their general hilarity as they confront these various "serious" states.
The song begins with an explicit sense of paranoia and insanity—the backing vocal "I may be paranoid, but not an android" and "unborn chicken voices in my head" suggesting hallucinations or, obviously, voices in the speaker's head. While not explicitly criticizing "yuppies" as later verses do, the "endless noise" opposing the speaker's desire for "REST" evokes the workaholic jungle of the modern city. In this context, the idea of the "android" may be that of a machine that doesn't require sleep or rest, or might represent how people treat themselves when they become entirely devoted to their careers.
The speaker's insanity and paranoia morph into a violent and Orwellian power trip in the next verse, erupting in sync with the distorted guitar at:
You don't remember
You don't remember
Why don't you remember my name?
Off with his head, man
Off with his head
So where's the humor here? While the song's title alludes to The Hitchhiker’s Guide to the Galaxy, the line "off with his head, man" comes straight from Alice in Wonderland and other fairy tales. Given the social criticism contained in the lyrics, one might expect real calls for violence but instead the speaker gives us ironically comical ones. It's as though the comedic relief is a warning to not take the song too seriously. (John Lennon did the same—and borrowed similar Lewis Carroll imagery to do so—in "I Am the Walrus.")
The verse that begins with "'that's it sir, you're leaving" contains more of the same—a mixing a social criticism with insane mutterings. You can practically see the speaker losing it as he sings "the panic / the vomit / the panic / the vomit." This verse is also where any antagonists are directly alluded to. For one, the mention of the "yuppies networking" in between the panic of "the dust and the screaming" and "the panic" implies connections between yuppie culture and the sources of the speaker's insanity, which were only alluded to in the beginning of the song. The only other time where there's an identifiable target in the song is in the line "kicking squealing Gucci little piggy," where the speaker "brands" the woman harshly on the sole basis of what she wears.