We know that the earth exerts a normal force equal to our weight on us . Now if somehow we harness the normal force and use it to do some other work (for example to produce electricity) then what would happen . I mean what effect would it have on us. Would we get deformed due to the exta force as we can't get accelerated downwards as there is the Earth's surface.
I think you meant that the surface on which we stand exerts equal and opposite force to balance gravitational pull, which we call as a normal force. If you have this understanding than you are correct about this statement, as it is important to distinguish that it is not the Earth that exerts a normal force, but the surface on which we stand. For example, if you stand on a table that is strong enough to hold you, it prevents you to fall further down as it is strong enough to provide the normal force that will balance your weight. Instead, if you try standing on water, you know what will happen! That's because the surface of the water is not hard enough to provide you with the necessary normal force.
So, here you need to understand that normal force always exists as a response to weight. If you place a 2 g weight on a table, the normal force will be less as compared to placing a 2 kg weight. As you increase the weight of an object placed (consider a bucket kept on the table which is getting filled with water) the normal force will also increase until a point where the surface is not strong enough to hold the object. Just think about this, can you harness any energy from a force whose mere existence is as a consequence of the existence of another force? You can't.
I hope I have understood your question, if not, please elaborate.
We would break the ground.
The example is clearer if you try to put a heavy object (lead ball) on a sheet of paper, and on a table. They both exert a normal force (which, by the way, isn't even a real force: like friction, it is an effect of the electromagnetic force between the molecules of the different objects) on the ball, but the one exerted by the table is enough to "stop" the ball, while the one of the sheet of paper is not. Therefore, the ball continue its path towards the center of the earth, until it's stopped by something else, the ground for example.
The normal force is pretty much just an interaction between two things that are "touching". So, I guess you could use this to harness energy? For example, a water wheel spinning relies on the normal force between the water and the water wheel in order to spin. In this case the normal force is large enough to spin the water wheel.
But it isn't like we have some secret untapped energy just waiting to be harnessed that is hidden within normal forces. They are forces that just arise from objects being close enough together so that there is a repulsion.