The human body is already very elastic. Your skin is amazingly stretchy. Most of your soft tissues and organs can be moved around to a significant extent. The most significant limitation on our ability to contort is those big, hard things inside of us that don't bend, known to the lay man as bones. Cephalopods such as octopods and squids, have no bones at all. This allows them to squeeze through tiny cracks with no issues. Clearly the issue with stretching and squeezing is caused by our skeletons.
However, having bones that are stretchy or bendy (or no bones at all) would be a major disadvantage. The skull has to be rigid to prevent the brain from being bruised or squashed. A solid ribcage protects most of your other vital organs. And strong leg bones are necessary for our terrestrial locomotion.
Some animals have much more flexible skeletons. Rats, for example, have solid bones like us, but they lack collar bones and their ribs have flexible joints at the spine. This allows them to squeeze through holes that are smaller than they are. Snakes are able to to eat things bigger than they are because they can move their bones apart. Their jaw is made up of three bones, which are only loosely connected, and their ribs will bend away from their spine in order to make room for what they swallow.
With a little more flexibility around the joints, it is possible to twist the body a great deal. Contortionists have the same bones as normal people.
The answer for the second part of your question is a little trickier. Some of the benefits I can think of are related to the environment your human variants are native to. If they live in a place with lots of narrow caves or tunnels, being able to stretch could be a big advantage in gathering food and escaping predators. Alternatively, it could be motivated by reproduction - perhaps elasticity is a marker that females use for sexual selection.