The structure of neutron-rich 96,98 Sr nuclei was investigated by low-energy safe Coulomb excitation of radioactive beams at the REX-ISOLDE facility, CERN, with the MINIBALL spectrometer. A rich set of transitional and diagonal E2 matrix elements, including those for non-yrast structures, has been extracted from the differential Coulomb-excitation cross sections. The results support the scenario of a shape transition at N = 60, giving rise to the coexistence of a highly deformed prolate and a spherical configuration in 98 Sr, and are compared to predictions from several theoretical calculations. The experimental data suggest a significant contribution of the triaxal degree of freedom in the ground state of both isotopes. In addition, experimental information on low-lying states in 98 Rb has been obtained.