Mmmm, interesting question.
The first approximation could be the following: simply divide your character into a set of physical bodies. I mean, you could calculate resultant force on legs, feet, arms and hands and operate with the results.
Think in Rayman, for example. It can be a good model to start with. The character would be formed by head, body, hands and feet. Every component would be attached to the body with a rope-like object (so if you make a lot of force in the body, the other parts will also be affected and viceversa).
For example, if you pull a hand with a external force, the hand will move. But also a elastic force would appear to the hand, proportional to body distance. This will limit the separation. Also a proportional force would appear on body, pulling our character...
I think you get the basic idea.
Of course, if you add more elements, your model will be more realistic, but it will be also difficult to calculate.
Also, you can be a bit tricky. Looks like you want a character that reacts realistically to extern media. The examples you mentioned could be solved using a "walk force" (the force the body do in another body when it walk into it) proportional to walk speed, so if the player runs it will be able to move the stone.
For the falls, simply divide your sprite into regions, get the collision angle and play an addecuate animation. You could have a set of 2-3 animations and make some changes (angle fall or speed) via code to make look it realistic.
And believe me: a good animation with an appropiate walk speed can emulate perfectly muscle movement and physical behaviour of your character, if you code it well.
Hope this give you some ideas. It may not be the anwser you were expecting, but I think you first have to plan which simulation method are you going to use in detail :D