A generalized formulation is developed for nonlinear acoustic solitons in three-component such as dust-ion-electron and electron-positron-ion plasmas with the charge of each species being unspecified. The heavy, cold charged particles (ions or dust particles) are treated as a fluid while the light, hot components are described by the kinetic Vlasov equation with separate velocity distributions which can be of function or highly nonthermal (non-monotonic) distributions. The model is also applicable for two-component such as ion-electron plasmas with two different temperatures for electrons. The generalized dispersion relation for acoustic waves and the Korteweg-de Vries equations as well as the Sagdeev potential are derived for various models with different combinations of velocity distributions. The parameter regimes for the existence of acoustic solitons are analyzed and examples of nonlinear solutions are illustrated. The polarity of electric potential is found to exhibit anomaly for highly nonthermal cases.