The phase behavior of the binary mixture of an anionic surfactant Aerosol OT (AOT) and glycerol (used as a model for water) is investigated using rheological, optical, and X-ray synchrotron techniques. In particular, the storage shear modulus G' response, as a function of temperature and strain amplitude, has been related to the structural transformation into the lamellar L-alpha phase surfactant bilayers. Results demonstrate a characteristic critical behavior at the phase transition boundary T = T-c. Stress-strain variation indicates the shear-induced alignment of the layer system with a universal scaling of stress-strain.