Stress-Strain curve 
(Point A shows proportional limit, B shows elastic limit, C shows UTS point, D shows fracture stress)
So I've read that stress is basically the result of strain acting on a body and that strain is applied first, then comes the stress. I've also read that after the elastic limit is surpassed, the stress is less and the strain is more. If it really is like that, the stress-strain graph (representing the modulus) should decrease, yet after point B, the graph increases till Point C. (Using formula E=stress/strain) Can someone explain?
 A: So I've read that stress is basically the result of strain acting on a body and that strain is applied first, then comes the stress. 
Actually, you have it reversed. Strain is the result of stress, not the other way around.
Ive also read that after the elastic limit is surpassed, The stress is less, the strain is more.
That is not correct. The increase in stress is less to cause an increase in strain. In other words, the curve is bending downward.
The elastic limit is the maximum stress, or force per unit area within a solid material before the onset of permanent deformation.  Up to that point, if the stress is removed the material will return to its original size, meaning the deformation (strain) under load will not remain after the load is removed. Beyond the elastic limit there will be permanent deformation after the load is removed. 
If it really is like that, then the stress/strain graph (representing the modules) should decrease, yet after point B, the graph increases till Point C. (Using formula E=stress/strain) Can someone explain?
It is not decreasing but notice that after the elastic limit (point B) it takes less increase in stress to cause an increase in strain. 
Hope this helps.
