The previous entry detailing the 'everything is in Peter's head' theory is great but super-depressing. Taking inspiration from that theory, some fans thought that it made more logical sense for the show to be taking place purely from Stewie's point of view rather than Peter's. Since everything is viewed from Stewie's perspective, he thinks he's smarter and better than everyone else on Earth, thus explaining his 'laboratory' and his apparent intelligence. Peter is your average goofy but lovable dad who acts childish around his kids, hence Stewie sees him as a bit of an exaggerated moron who gets up to wild antics all the time. Lois is the strict mother who bathes and feeds him, but seeing how children generally don't like baths or eating healthy food, Stewie sees her as a devil who must be vanquished. Meg and Chris don't feature too much since they're teenagers and they have lives outside of spending time with Stewie. As for Brian, he's considered Stewie's best friend since he's a dog and has a similar intelligence level comparable to a baby. As for the self-referential nature of the show, that can be simply explained by Stewie's inability to grasp what's going on in the real-world and pop-culture references are a sort of coping mechanism.
My life story is nothing special. I haven't cured ebola, I'm nowhere near stopping terrorism, and I'm still working on that climate change problem.
Instead, all I've done so far is put a few hundred words together in an attempt to make people laugh.
You can follow me at @Fry_ying_pan but don't be offended if I don't tweet back. It's usually because I've spent too long trying to think up a witty response that the reply window has closed.