We consider two classes of t-b-tau quasi-Yukawa unification scenarios which can arise from realistic supersymmetric SO(10) and SU(4)(C) x SU(2)(L) x SU(2)(R) models. We show that these scenarios can be successfully implemented in the nonuniversal Higgs model with m(Hu) = m(Hd) not equal m(0) and the constrained minimal sumersymmetric model frameworks, and they yield a variety of sparticle spectra with Wilkinson Microwave Anisotropy Probe compatible neutralino dark matter. In the nonuniversal Higgs model with m(Hu) = m(Hd) not equal m(0), we find bino-Higgsino dark matter as well as the stau coannihilation and A-funnel solutions. The constrained minimal sumersymmetric model case yields the stau coannihilation and A-funnel solutions. The gluino and squark masses are found to lie in the TeV range.