The Young Ones/WMG

The Balowskis and their lookalikes were grown on a secret Soviet clone farm.
The farm was located in a defunct section of the London Underground. It was discovered and infiltrated by MI5 sometime prior to the start of the series. Unfortunately, the self-aware clones escaped in the ensuing siege and took up residence above ground. Most of them took the code name of the project, "Balowski", as a surname, but trained themselves to act British (with varying degrees of success) so as not to invite suspicion.

Vyvyan's father is a Weasley (but not any of the ones we know).
Bright red hair? Check. Propensity for mischief? Check. Clever and inventive? Check. Taste in automobiles? Ford Anglia. The Weasleys are fascinated with and freely associate with Muggles, so it's not entirely impossible that one of them could have had a brief dalliance with a Muggle woman. If we assume that Vyv is 19 in 1982, he would have been born around 1963. Therefore, Arthur Weasley (born in 1950) would have been too young. However, the books state that Arthur had at least two brothers, and if one or both of them were significantly older, they would be likely candidates. Even though Vyv is a Muggle for all intents and purposes, this theory could account for his enhanced abilities (occasional Super Strength, Hard Head-edness, ability to ingest poisons and non-edible items with no ill effects) as well as his ridiculous Healing Factor.
 * Bilius (Ron Bilius' namesake). Although it was never explicitly stated whether he was Arthur's or Molly's brother, many fans presume him to be a Weasley. Very little is divulged of him, except that he was prone to outrageous behavior -- namely, getting drunk and raising hell. His name is derived from the word "bilious", which indicates the classical personality type associated with an excess of yellow bile, and thus is a synonym for "choleric". In the show's Four Temperament Ensemble, Vyvyan occupies the Choleric corner.

One day the boys will get their own movie and cross over with, Danger Days.
I hope so at least.

The characters in the Young Ones are like the countries from Scandinavia and the World, but they personify decades.
Mike is the Fifties, Neil is the Sixties, Vyvyan is the Seventies, and Rick is the Eighties.
 * Alternatively, except for Rick, they're time travellers from different decades that wind up in the Eighties, which is why they hate Rick so much.

At least one of the lads, or Balowskis, is unknowingly a Reality Warper.
It’s the only way in heaven, hell, or on earth this show could ever make sense.

Vyvyan knew he had trapped wind the whole time; he just used his flatmates’ stupidity to his advantage.
He’s been hinted to be Obfuscating Stupidity more than once by this point in the series, shown to be more than willing to manipulate people to achieve his ends, and is obviously secure enough to let himself blow up like a balloon and lead the other lads on, as long as it meant he wouldn't be the one to have to try and get a job. By the time the problem resolved itself and his cover was blown, it didn’t matter, because Neil had already taken the hit. Completely brilliant!