We employ the techniques of microparticle image velocimetry and full-field birefringence microscopy combined with mechanical measurements of the pressure drop to perform a detailed characterization of the extensional rheology and elastic flow instabilities observed for a range of wormlike micellar solutions flowing through a microfluidic cross-slot device. As the flow rate through the device is increased, the flow first bifurcates from a steady symmetric to a steady asymmetric configuration characterized by a birefringent strand of highly aligned micellar chains oriented along the shear-free centerline of the flow field. At higher flow rates the flow becomes three dimensional and time dependent and is characterized by aperiodic spatiotemporal fluctuations of the birefringent strand. The extensional properties and critical conditions for the onset of flow instabilities in the fluids are highly dependent on the fluid formulation (surfactant concentration and ionic strength) and the resulting changes in the linear viscoelasticity and nonlinear shear rheology of the fluids. By combining the measurements of critical conditions for the flow transitions with the viscometric material properties and the degree of shear-thinning characterizing each test fluid, it is possible to construct a stability diagram for viscoelastic flow of complex fluids in the cross-slot geometry.