There is one more force that you probably have not considered, and that is the normal force. Since they are on the floor the floor is exerting a force on the objects equal to that of the gravitational force so that the objects don't infinitely accelerate towards the center of the Earth.
So for object 2, when the force is applied the normal force decreases so that the normal force plus the 25N is equal to the gravitational force.
Object 1, 3, and 4 all move since the force applied is greater than the gravitational force. Object 3 moves the fastest since it has the smallest weight.