How does the system of particles respond to the external force? If I push a box forward, then probably, the force I apply can be considered external force acting on the system of particles of the box. In rigid bodies like the box, each particle of the body should experience some force and as a result of the interaction of applied force with each particle of the body there is a net external force which will move the object forward. (Do correct me if I'm wrong.)
But I kept wondering that if I'm applying the force to certain portion of the box then the forces will be experienced only by the particles directly in contact with my hands. Then how does other particles of the rigid object experience force? Is it related to intermolecular forces?
 A: At the instant you apply a force onto a part of the body, the intermolecular electrostatic forces will cause the force to propagate along the body. One could think of it as a 'ripple effect' propagating through the solid Now if the force is applied such that the line of action of the force does not pass through its center of mass, then the body will also experience a torque, or a turning effect. If the torque is sufficient, you may even observe that the block topples while you push it.
A: First of all, rigid body is an assumption. There is no real rigid body exists. 
If you consider box as a rigid body, you are right, the external force will be distributed among all the particles of the system in such a way the acceleration of all the particles of the system is same.
But, I think from your question, it looks like you want to know about the real object and not just an ideal rigid body. In that case, the body will experience some deformation, elongation, shear etc. If you mean to know answers to that I would say that there is course of "Mechanics of Solids (MOS)" in the first and second year of the Mechanical engineering. If you want to study this, I could suggest you some good books.
