stress strain curve details

Wherever there is stress there is strain.

In the example you noted, if heated bar expands freely without one end constained it changes its strain without stress; that strain is called eigenstrain.

If the same bar is held rigidly then the eigenstrain resisted and you get stress and strain. So stress cannot exist without strain; but strain can exist without stress if it is eigenstrain.

stress is load per unit area; when an object is loaded it is under stress and strain and it stretches (strains) until it breaks at its ultimate strength. Stress i srelated to strain in the elastic region by Hooke's law: stress = elastic modulus times strain where modulus is a property of the material and strain is deflection over length

stress is directly proportional to strain up to the proportional limit. Their ratio is young's modulus.

The strain gage indicates strain, and the stress is from Hooke's law; stress = modulus times strain so you need to know the modulus of elasticity