We report photoassociation spectroscopy of ultracold Sr-86 atoms near the intercombination line and provide theoretical models to describe the obtained bound-state energies. We show that using only the molecular states correlating with the S-1(0) + P-3(1) asymptote is insufficient to provide a mass-scaled theoretical model that would reproduce the bound-state energies for all isotopes investigated to date: Sr-84, Sr-86, and Sr-88. We attribute that to the recently discovered avoided crossing between the S-1(0) + P-3(1) 0(u)(+) ((3)Pi(u)) and S-1(0) + D-1(2) 0(u)(+) ((1)Sigma(+)(u)) potential curves at short range and we build a mass-scaled interaction model that quantitatively reproduces the available 0(u)(+) and 1(u) bound-state energies for the three stable bosonic isotopes. We also provide isotope-specific two-channel models that incorporate the rotational (Coriolis) mixing between the 0(u)(+) and 1(u) curves which, while not mass scaled, are capable of quantitatively describing the vibrational splittings observed in experiment. We find that the use of state-of-the-art ab initio potential curves significantly improves the quantitative description of the Coriolis mixing between the two -8-GHz bound states in Sr-88 over the previously used model potentials. We show that one of the recently reported energy levels in Sr-84 does not follow the long-range bound-state series and theorize on the possible causes. Finally, we give the Coriolis-mixing angles and linear Zeeman coefficients for all of the photoassociation lines. The long-range van der Waals coefficients C-6(0(u)(+)) = 3868(50) a.u. and C-6(1(u)) = 4085(50) a.u. are reported.