The electric-dipole and quadrupole polarizabilities of the 5s5p 3P1 degrees 1 state and the C-6 and C-8 coefficients for the S-1(0) + S-1(0) and S-1(0) + P-3(1)degrees dimers of strontium are calculated using a high- precision relativistic approach that combines configuration interaction and linearized coupled-cluster methods. Our recommended values of the long-range dispersion coefficients for the 0(u) and 1(u) energy levels are C-6(0(u)) = 3771(32) a.u. and C-6(1(u)) = 4001(33) a. u., respectively. They are in good agreement with recent results from experimental photoassociation data. We also calculate C-8 coefficients for Sr dimers, which are needed for precise determination of long-range interaction potential. We confirm the experimental value for the magic wavelength, where the Stark shift on the S-1(0)-P-3(1)degrees transition vanishes. The accuracy of calculations is analyzed and uncertainties are assigned to all quantities reported in this work.