Learn English – The meaning of “you are a smash”

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.

"Down with" is simply an idiom, used to express negative emotions toward something. A close cousin of "Down with homework" could be "Say no to homework". You might hear protesters use this kind of language while chanting at a demonstration (it's short, and to the point); it also makes it way onto T-shirts, and even magazine covers from time to time.