The acoustic de Haas-van Alphen (dHvA) effect and temperature dependence of the transverse mode (C-11 - C-12)/2 have been measured in a layered Perovskite superconductor Sr2RUO4 With T-c* = 1.42 K. From the acoustic dHvA oscillations for alpha and beta orbits along [001], the area coefficients are estimated to be \Lambda (alpha)(B1g)\ = 0.8 and \Lambda (beta)(B1g)\ = 0.2 similar to 0.3. Both Fermi surfaces consisting of hybridized Ru-4d(xx(yz)) orbitals couple weakly to epsilon (xx) - epsilon (yy), because the in-plane shear strain hardly varies the spacing between the alternating RuO2 layers. Large softening occurs below 220 K, which corresponds to the rotational instability. The rotational deformation of the RuO6 octahedron is induced perturbingly by epsilon (xx) - epsilon (yy) which reduces the lattice matching.