For the jelly look of the platforms you can use equations for springs to get a nice effect. Canvas or Paster would be needed if you want a more pleasing appearance,
Drag the points around.
Collision response with a player will require more math for the collision response, but it basically boils down to checking the player's collision with the edges and pushing each other out just enough so they are no longer overlapping. There is a bit more to it but it would have to wait till I revisit this and push it further.