Ultrasound velocity measurements based on a phase comparison method for four different modes have been done on a copper-free layered perovskite superconductor Sr2RuO4 With T-c = 1.2 K. Anomalous softening is observed in the longitudinal C-11 and C-33 modes below 108 K, which is attributed to the coupling of the electronic states to the strain with Gamma(1) representation in the tetragonal point group D-4h The discontinuous change of the slope in C-11 and C-33 at Te is basically explained by the second-order strain dependence of T-c, partial derivative(2)T(c)/partial derivative epsilon(uk)(2). From the initial slope of the upper critical field H-c2, the anisotropy ratio in the coherence length is found to he 28, in agreement with previous ac susceptibility measurements. Acoustic de Haas-van Alphen oscillations for the cylindrical alpha-Fermi surface with 3.2m(0) are observed in C-33 as a function of the magnetic field applied perpendicular to the Q2D conducting plane. The area coefficient is evaluated to be \Lambda(zz)\ = 20+/-5 from the Kataoka-Goto model. The multiband term \Lambda(zz)(m)\ contributes dominantly to \Lambda(zz)\, which corresponds to the interband charge transfer.