Material Stress and strain

The relationship between the stress and strain that a particular material displays is known as that particular material's Stress-Strain curve. It is unique for each material and is found by recording the amount of deformation (strain) at distinct intervals of tensile or compressive loading (stress). These curves reveal many of the properties of a material (including data to establish the Modulus of Elasticity, E).^[1]

Source : http://en.wikipedia.org/wiki/Stress_and_strain
Read more here.

I found a useful video on youtube

Hope the video was useful. I thing he has covered the topic pretty well. 

What is the differences between true strain & engineering strain and true stress & engineering stress?

 Engineering strain is ratio of change in length to the original length.
True strain is defined as the natural logarithm of instantaneous length to original length.

Engineering stress assumes that the area a force is acting upon remains constant, true stress takes into account the variation in the cross sectional area as a result of the stress induced deformation (strain) of a material.

More precisely
Engineering stress is the applied load divided by the original cross-sectional area of a material. Also known as nominal stress.
True stress is the applied load divided by the actual cross-sectional area (the changing area with respect to time) of the specimen at that load
Engineering strain is the amount that a material deforms per unit length in a tensile test. Also known as nominal strain.
True strain equals the natural log of the quotient of current length over the original length.

Formulae

Here is a video I picked up on you tube. It explains the engineering strain, engineering stress , true strain and true stress and their relationship