Definitions of stress and strain
Nominal stress: the force on the object divided by the original area.
True stress: the force on the object divided by the actual area. E.g., when necking occurs the true stress is the force applied divided by the area of the neck.
The unit for stress is Nm-2, or Pa.
Nominal strain: change in dimension / original dimension
This is also known as the engineering strain, and is strictly only true for very small displacements. For large displacements, true strain should really be used.
True strain: loge [deformed length / original length]
True strain is applicable for larger strains, but tends to be more difficult to apply than nominal strain. Is also be known as the logarithmic strain. This remains a ratio, and so does not have any units.
There are no units for strain since it is a pure ratio.