<p>In this paper, we investigate a forced variable-coefficient Gardner equation in a fluid or plasma. Via a reduction of that equation, we get certain traveling wave solutions and Painlevé-integrable constraints of that equation. Multiple real, complex and singular soliton solutions are obtained via the simplified Hirota’s method. Such analytic solutions as the bell, kink, singular, combined and periodic soliton solutions are derived with the help of the solitary wave ansatz method. Breather and breather-soliton interaction solutions are derived via the multiple real soliton solutions. Moreover, we illustrate the effects of the variable coefficients on those nonlinear waves graphically: (i) the external force affects the backgrounds of those nonlinear waves; (ii) the damping coefficient affects the amplitudes and velocities of those nonlinear waves; and (iii) the cubic nonlinear coefficient and dissipative coefficient affect the characteristic lines, positions and velocities of those nonlinear waves.</p>