Is it really possible to lift and carry something that outweighs you? If so, which muscles are most important for lifting and carrying it? Just legs and core? Or do you need strong arms and chest muscles as well?

I am gonna be honest with you... I don't think it matters the size or placement of muscles. I believe it is a matter of the brain and heart. If your brain tells you you can do it, then chances are you will. (Maybe with injury but still... Gotta be smart. Lol!) As far as the heart.... Have you ever heard stories of petite mothers lifting up a car from on top of their child? It happens. The heart of a parent gives them super powers when it comes to their children. 😊

Yes, it is.

Strength is needed in every muscle group affected by the type of lift.

Something that outweighs you---yes. Generally speaking; but at my age (73) I would have to train for a while first to prepare my body for such a demand---with emphasis on the muscles I would be using. 

Superhuman lifting can occur, but frequently with damage to one's body that is not realized or felt until a while after the incident.

https://www.psychologytoday.com/us/articles/201011/stealth-super-powers