The formation and propagation dynamics of the finite-amplitude ion-acoustic wave (IAW) structures (e.g., soliton, breather, rogue wave, etc.) is theoretically investigated in a plasma comprising of kappa distributed solar and cometary electrons of different temperatures, a hot $$$ {\mathrm{H}}_3{\mathrm{O}}^{+} $$$ drift ion component, and a pair of oppositely charged oxygen ion components. The modified-KdV (mKdV) equation is derived in order to study the propagation dynamics of the ion-acoustic solitary wave (IASW). It is then converted into the nonlinear Schrödinger equation (NLS) through appropriate algebraic manipulation in order to observe the amplitude modulation of the IAWs. Also, the appearance of envelope soliton and the possibility of breather structure formation have been studied from the NLS equation. The dependence of plasma parameters on the formation and propagation of IAW structures has been briefly discussed. The modified-KdV equation is reduced in a dynamical system through the application of coordinate transformation. The existence of finite-amplitude nonlinear and supernonlinear IAWs is demonstrated by phase plane analysis. Due to the fact that the results are primarily associated with cometary plasma, they possibly provide greater insight of the nonlinear characteristics of cometary plasma.