It takes many listens for it to fully settle in that Andy, Akiva, and Jorma, when 13 years old, got drunk off Martian wine and then proceeded to have sex with a male alien at the same time so that they could repopulate a dying alien race with their sperm.
And while the alien did initially leave the trio with much MC swag ("Jack Sparrow", and "Turtleneck & Chain"), the whole event apparently left the boys with varying forms of penile dysfunction ("Jizz in My Pants", "We're Back", and "I Just Had Sex"). This results in their failure to find success with beautiful women no matter what, even when the ladies themselves try to take the initiative ("Attracted to Us"). Out of desperation, the guys aim for something much lower on the scale ("Dreamgirl"), but that also fails. The lack of any decently meaningful relationships in the boys' lives turns them certifiably insane at one point, and they proceed to lose whatever street cred they had ("Who Says We're Wack?") by doing generally insane things ("Trouble on Dookie Island", "Punch You in the Jeans", "The Creep"). Samberg soon develops extreme bi-polarity that leads to a lifestyle of constant self-mutilation ("Like a Boss"), while Akiva and Jorma kinda settle on being dorks with no real social skills ("We Like Sportz"). Eventually, the trio realize that they need to deal with the issue once and for all, but that also ends up failing to produce any real favorable results ("After Party").
The Boss's crazier actions (like chopping his balls off and bombing Russians) can be traced all the way back to getting rejected by his co-worker.
Everything from "crash my car" onwards can be explained as hallicunations from a combination of drugs & alohol, emotional stress and injuries from falling out of a window and... well, crashing his car...