Learn English – What does “to go to school on someone” mean

To "pull one's leg", as a saying, does seem to have the etymology you describe; every source I can find states that it dates back to the mid-1800s in England, and refers to physically tripping up another person, which puts him off balance, possibly makes him collide with others in awkward ways, and generally makes him look foolish. It quickly evolved to mean achieving that result - making a person look foolish - regardless of the specific means used. The most popular means to do so is to tell a deliberate plausible non-truth which, if believed, would lead the person react foolishly.

"Pulling one's plonker" by contrast seems to be a much newer term, still considered slang and rare in American usage (it's most common in British and Australian vernacular). It's one of many examples of introducing a sexual connotation to otherwise "innocent" idioms and sayings.

The phrase stir the paint is not standard slang. It cannot be found in this UK dictionary of slang, this slang site, this other slang dictionary, or this published dictionary of slang. However, there are similar phrases which have sexual meanings. According to the Cassell's Dictionary of Slang, these are some of the slang uses of stir as a verb:

• stir fudge--1960s, to perform anal intercourse

• stir it up--1950s, to masturbate

• stir one's stew, stir the batter, stir the sauce--1950s+, see stir it up

• stir shit--go out of one's way to make trouble

• stir the porridge--1980s, Australia, to have sexual intercourse with a woman immediately after she has had intercourse with another man, esp. used of the final man in a gang-rape

• stir the possum--to create a disturbance

• stir the stew--1900-1910s, to have sexual intercourse

So there is a highly sexual connotation to stir that has been around since the 1900s. It seems likely that stir the paint is similarly sexual, although it is not documented before the Family Guy episode aired. Thus it is also likely that Family Guy coined the phrase, but did so based on these preexisting meanings. I would hazard a guess that the "paint" is menstrual blood.

It is similarly possible that stir the paint is not sexual at all, but instead refers to some dynamic between the two parents in which Lois will not let Peter do tiny things like stir paint, but given the nature of the humor in Family Guy I doubt this.