Let's consider each species in List I and determine their geometries/shapes.

A. $\mathrm{H_3O^+}$: This ion is formed by the addition of a proton to a water molecule. The central atom (O) is surrounded by three Hydrogen atoms and one lone pair, making its shape pyramidal.

B. Acetylide anion: The acetylide ion ($\mathrm{C_2H^-}$ or $\mathrm{C_2^{2-}}$) has a linear geometry as the three atoms are in a straight line.

C. $\mathrm{NH_4^+}$: The ammonium ion has a central nitrogen atom surrounded by four hydrogen atoms, giving it a tetrahedral geometry.

D. $\mathrm{ClO_2^-}$: The chlorite ion has a central chlorine atom surrounded by two oxygen atoms and one lone pair, which gives it a bent or V-shaped geometry.

Matching these to List II, we get:

A. $\mathrm{H_3O^+}$ - III. Pyramidal

B. Acetylide anion - II. Linear

C. $\mathrm{NH_4^+}$ - I. Tetrahedral

D. $\mathrm{ClO_2^-}$ - IV. Bent