A general formulation is proposed for electrostatic solitons in multicomponent plasmas consisting of one cold species described by the fluid model and multiple hot components described by the kinetic equation. For hot species two types of generalized velocity distributions are adopted: the kappa function and the highly nonthermal distribution with two free parameters which incorporate the widely used nonthermal distribution proposed by Cairns et al (1995 Geophys. Res. Lett. 22 2709) as a special limit. The general expressions for the KdV equations and the Sagdeev potential, as well as the conditions for electrostatic solitons with positive or negative polarity, are derived, which may give rise to various solutions for acoustic solitons in multicomponent plasmas with generalized nonthermal velocity distributions.