We discuss the charged and neutral fermion masses and mixings in a supersymmetric SO(10) model with a minimal Higgs sector consisting of the multiplets 10H, 45H, and \({16}_{H}+{\overline{16} }_{H}\) . In addition to the renormalizable Yukawa couplings involving the Higgs 10-plet, we include non-renormalizable Yukawa couplings, which are important for reproducing with good accuracy the observed masses and mixings in the quark and lepton sectors. We identify a preferred solution which is compatible with third family quasi-Yukawa unification, namely yt ≈ yb ≈ 0.73yτ at the unification scale, with the MSSM parameter tan β ~ 58. Acceptable solutions with lower tan β values are also realized in our framework, and we provide an example with tan β = 10. Based on our fits, the masses for the three right-handed neutrinos turn out to be (M1, M2, M3) ~ (109, 8∙1012, 9∙1012) GeV. We briefly discuss the metastable and quasistable string scenarios that can be realized in this class of supersymmetric SO(10) models.