Chinese ostrich
鴕 centers on a specific large bird: the Chinese ostrich. It is a narrow zoological term with no extended abstract meanings.
鴕 combines 鳥 (bird) with 它, which likely contributes the sound. The character was created to name a specific bird, the Chinese ostrich.
The left side is a bird 鳥, and the right side 它 looks like a large, long-necked creature. Picture a bird with an ostrich-like silhouette: 鴕 is the Chinese ostrich.
For ダ, imagine a large ostrich dashing across the plain: dash -> ダ, and the bird's speed matches the sound.