Is the storyline of Family Guy reset with every episode?

Sometimes. There seems to be some canonic events, like Bonnie having her baby, and Cleveland moving away. At the same time, there are other things, like when characters are brutally beaten or hospitalized, that get waived between episodes.

Family guy like many othet animated comedy shows are ‚episodic‘ where each episode has a contained central story, where only some events may be carried over to following episodes or subsequent seasons.

This was also often called ‚bottled episodes‘ for other shows like X-files and older star trek....and countless other shows, however this Trend was replaced with season long stories favoured and arguably inspired the most by Breaking Bad.

The common explanation for shows having little continuity from episode to episode is called -TRV TROPES WARNING - hitting the reset button.

https://tvtropes.org/pmwiki/pmwiki.php/Main/ResetButton[1]

But I want to offer an alternate explanation for lack of continuity in many tv shows.

In my opinion, you can think of the events in an epsode of a highly episodic and long running series as being something which could possibly happen to the characters given the initial set up and the laws of science and/or magic which may exist in the series, and which will thus happen to the characters in at least a few of the countless alternate universes they exist in.

Thus the creators of the show would serch through thousands and millions and billions of alternate universes which diverge over time from the single universe where the show's situation begins, looking for interesting stories happening to the characters. And they would select tens or hundreds of the most intersting stories from different alternate universes to depict.

So each episode should happen in an alternate universe of its own, except for episodes which are prequels and sequels to each other.

I don't know what percentage of early television writers and producers were familiar with the science fiction concept of alternate universes, but I guess that their general concept was that each episode aof a highly episodic series was something which could happen to the characters - and not that all of the episodes would happen, one after the other, in the the order that they were created (or the order that they were broadscast in) in one fictional universe.

And and a fan can think that when there is a major and permanet change in the setting, such as the characters moving, new major characters arriving, or old characters departing, etc., that would happen in only one alternate universe, and the following episodes where the change is acknowledges are all selected from the many alternate universes which branch off from the change, and not from alternate universes where the change never happened.

The common idea is that the "rest button" is pushed at the end of each episode, and the situation returns to the original situation, But my alernate universes theory says that each episode can have permanent consequences, but since it is rare to show a sequal episode in the same alternate universe, the viewers never see the permanent consequences of most episodes. Most of the following episodes will be selected from alternate universes where that episode never happened and so couldn't have consequences.

I developed this theory for Star Trek: The Original Series (1966-1969) to explain various features of that series, such as how the protagonists could survive themany dangers they faced during the series.

But that theory can equally apply to futuristic science fiction, contemporary shows, or shows set in past historical eras. It can apply to adventure series, drama series, comedy series, or any other genre.

Except for highly serialized soap operas and similar shows in the past. And with present trends in making drama and even comedy shows more serialized and less episodic, it is becoming less applicable to more modern shows.

But it is still applicable to a number of modern tv shows. For example, the sitcom The Goldbergs (2013-) has many episodes where members of the Goldberg family realize how badly they are behaving, apologize, and promise to change their ways. But it never sems to stick and they keep repeating the same flawed behavior and repenting of it in episode after episode.

And that can be explained by the theory of "hitting the reset button" after each episode, or by the theory of many episodes happening in alternate unverses, so that each character can learn the same lession, repent, and change their behavior for the rest of their lives many different times in many different alternate universes.