Under investigation in this paper is an inhomogeneous higher-order nonlinear Schrodinger equation, which describes the transmission of the subpicosecond or femtosecond optical solitons in inhomogeneous optical fibers. Bilinear forms are obtained with the help of an auxiliary function. With symbolic computation, degenerate and nondegenerate solitons are derived. Solitons in the form of single-hump, double-hump and flat-top profiles are displayed. Soliton amplitude is affected by the third-order dispersion coefficient and self-steepening coefficient, while soliton velocity is only related to the third-order dispersion coefficient. Interactions between the two nondegenerate solitons are asymptotically discussed, including the periodic- and cross-interactions between a single-hump soliton and a double-hump soliton. Independent propagation and overtaking interaction happen between the two double-hump solitons. Solitons keep their shapes invariant after the cross-interactions, except for some phase shifts.