The film starts with a man named Henry Spencer (Jack Nance) hovering in space. His brain, represented by a rocky planet visible through his head, hovers behind him. On the rocky planet's desolate surface, there is an overhead view of a building with a large hole in the roof. In the building sitting by a window with broken glass there is a Man in the Planet (Jack Fisk) who pulls levers to control Henry's functions which represents his central nervous system. This scene is going to represent Henry having sexual intercourse with a woman named Mary X (Charlotte Stewart). Henry's mouth opens and a spermatozoon slides its way out, then rests erect at Henry's side. The Man in the Planet pulls several levers and launches the sperm into a water hole which represents the vagina of Mary X. Some time passes and a creature is born in the depths of blackness and rises to the surface.
The next scene starts with Henry looking at the camera. He then proceeds to walk home to his apartment through a slum in an industrial wasteland carrying a small brown paper bag. Henry stumbles past factories with heavy machinery roaring. There is carnival music heard in the distance, but there are no people or automobiles around anywhere. The sounds of a steam whistle, as well as a horn of a cargo ship are heard among the loud sounds of the machinery.
When Henry gets to the lobby, he checks the mail and finds there is none. He then takes the elevator up to his apartment which is Room 26. Before he gets inside, the Beautiful Girl Across the Hall (Judith Anna Roberts), who lives in Room 27, informs him that Mary X called from the payphone in the hallway and invited him to dinner. While in his apartment, Henry turns on some lights, sets down the brown paper bag containing paper-wrapped groceries, puts on light jazz music from a record player, takes off his shoes and puts one of his socks on the radiator since it was wet from stepping in a puddle while walking home. While sitting on his bed, he then stares at the hissing radiator which represents thoughts of suicide. We see that there are electrical wires around the radiator. He glances out at the only window in his one-room apartment which only has a view of a brick wall of another building across the alleyway, symbolizing his claustrophobic, prison-like setting. In the background is a small picture of a mushroom cloud which shows the setting to be a post-apocalyptic future. He then throws a stone in a pot of water in his dresser which is meant to be a superstitious gesture, and looks at a torn picture of Mary.
That evening after dark, Henry walks over to Mary's house through the industrial wasteland and through a railroad yard to meet her family and have dinner. Before he goes in, they mention Henry and Mary's strained relationship. While Henry is talking with Mrs. X (Jeanne Bates) in the living room, it's revealed that Henry works as printer at LaPell's Factory, but is "on vacation". Henry meeting the family is portrayed as very awkward throughout the scene. While Henry and Mary wait in the living room, Mary's father (Allen Joseph) works on cooking artificial chickens baking in the oven, while Mary's mother fixes a salad. An elderly woman, the Grandmother (Jean Lange), sits motionless in the kitchen. The family attempt to eat the artificial chickens and salad but everything goes wrong when the chickens start twitching and bleeding when Henry tries to carve them. After dinner, Mrs. X interrogates Henry about whether or not he had pre-marital sexual intercourse with Mary. He confirms that they did and it's revealed that Mary had a deformed, premature baby. Mrs. X orders that they must get married as soon as possible and pick up the baby from the hospital.
The next scene cuts to sometime later after they get married and get the mutated, alien baby home. Henry goes down to the lobby and checks the mail to find a small worm in a stylish black box. Henry hides this from Mary first in his pocket and later in a cupboard next to the bed. He gets home and contemplates suicide again, this time more seriously.
During the night, as Henry and Mary sleep, the baby cries continually. The sounds of a raging thunderstorm is heard from outside as well as sounds of more factory machinery and rumblings of a freight train are heard. Mary can't stand it and tells Henry that she is going back home, leaving Henry to deal with the baby.
The Beautiful Girl Across the Hall is seen returning to her apartment in a disheveled state after an apparently bad date. (It is implied that she may be a prostitute).
Over the next few days, Henry has trouble sleeping and hears the baby stop crying. He gets out of bed to check its temperature and after the temperature reads fine he looks back at the baby seeing that it is covered in sores and apparently sick. After he sets up a vaporizer, the Beautiful Girl Across the Hall comes over and seduces him and they literally melt into the bed. The Girl sees the mutated baby nearby crying.
The lady in the radiator (Laurel Near) appears again on a stage singing "in Heaven everything is fine" while mutated worms (symbolizing sperm) fall from the ceiling and she steps on them. Henry goes on stage and a dead tree in some dirt is wheeled out which makes him appear uneasy and he steps to the side of the stage where he acts agitated. As he plays with a railing staring off into space, his head pops off and the crying mutated baby takes its place. His head forms a pool of blood and eventually falls into it, re-appearing out of the sky and landing in an alley in the industrial wasteland.
A little boy (Thomas Coulson) sees Henry's severed head on the ground and takes it away with him to an eraser factory. When the boy arrives, Paul, (Darwin Joston), the taciturn mechanic working at the front counter, buzzes his ill-tempered Boss (Neil Moran) to the front where the Boss takes the little boy with Henry's severed head through another door and to a pencil machine operator (Hal Landon Jr.) in another back room where Henry's head is made into erasers for pencils.
Upon waking up from the nightmare, Henry hears something outside his apartment. He then sees the Beautiful Girl Across the Hall being intimate with a man named Mr. Roundheels (Raymond Walsh). When he gets back inside his apartment, the baby makes strange cackling sounds as though it's laughing at Henry. Henry, apparently agitated moves over to the baby and begins to cut off the bandages covering its body causing the baby to breathe heavily. To Henry's horror, the baby's body splits open as it was either too fragile or Henry had cut into it. Henry decides to stab into the baby's heart with the scissors and collapses on the other side of the room. The baby's innards flow over the electrical wires which then produce sparks and short-circuit the lights. He sees the baby's head hovering about on a now very long neck, as the lights flicker in and out the baby's head becomes gigantic and it engulfs the camera.
The man in the planet is seen pulling a lever and apparently being electrocuted. In the final shot, we see Henry standing in some kinds of white afterlife and embrace the woman in the radiator.
Alternate synopsis and possible reason for the weirdness:
It is an alternate world in the early 1970's. The United States was attacked by either the Japanese or Russians in the late 1940's or early 1950's; the Japanese having revenge for what we did in World War 2 or the Russians fulfilling our Cold War paranoia. As a result, over 95% of the population was wiped out. Little or no attempt was made to rebuild America and technology was halted to a standstill. It would appear that all electricity seems to be run on steam generators and factories are self-running. Henry lives in a 1940's era apartment with a 1978 record player and iron frame bed. And the X home looks like a relic of that era as well.
It is set in a small industrial town on the outskirts of Philadelphia or a small town in Pennsylvania in the early 1970's. The population of the town is probably no more than 100 people. Henry Spencer was a child when the atomic war happened. As a result of radiation poisoning and the trauma of the attack, he was socially awkward, prone to frequent hallucinations and fantasy worlds, and with autistic traits. The X family has many forms of mental illness. Mr. X is manic depressive/bipolar, Mrs. X is schizophrenic, Mary with epileptic fits and clinical depression, and Mrs. X's mother with dementia that became catatonia.
Because nearly all animal life was wiped out, nearly all food is synthetic or genetically modified.
As for the baby, 20 plus years of radiation poisoning had modified Mary's reproductive system. Bringing a child into the world has been discouraged for the past 20 years.
The lady in the radiator, man in the planet, and his head being made into erasers are all illusions Henry has for his miserable existence. At the end, he kills the baby, then presumably kills himself, but to him, it appeared the baby ate him and he ended up in heaven with the woman of his dreams.