Hyperfine structures and isotope shifts of strontium isotopes with A= 78 to A= 98 and A= 100 were measured by collinear fast beam laser spectroscopy. Nuclear spins, moments and changes in mean square charge radii are extracted from the data. The spins and moments of most of the odd isotopes are explained in the framework of the single particle model. The changes in mean square charge radii are compared with predictions of the droplet model and of Hartree-Fock-plus-BCS calculations. For the isotopes in the transitional regions below and above the N= 50 shell closure, the inclusion of quadrupole zero point motion in the Droplet model describes part of the observed shell effect. An additional change in the surface region of the charge distribution at spherical shape is suggested by the microscopic model. Furthermore, we propose that the isotopes Sr 78 and Sr 80 may show an unusual shape-sharing structure, with different mean deformations in the ground and 2 1+ excited states.