Calcium vanadate CaV$_2$O$_4$ has a crystal structure of quasi-one-dimensional zigzag chains composed of orbital-active V$^{3+}$ ions and undergoes successive structural and antiferromagnetic phase transitions at $T_ssim 140$ K and $T_N sim 70$ K, respectively. We perform ultrasound velocity measurements on a single crystal of CaV$_2$O$_4$. The temperature dependence of its shear elastic moduli exhibits huge Curie-type softening upon cooling that emerges above and below $T_s$ depending on the elastic mode. The softening above $T_s$ suggests the presence of either onsite Jahn-Teller-type or intersite ferro-type orbital fluctuations in the two inequivalent V$^{3+}$ zigzag chains. The softening below $T_s$ suggests the occurrence of a dimensional spin-state crossover, from quasi-one to three, that is driven by the spin-lattice coupling along the inter-zigzag-chain orthogonal direction. The successive emergence of the orbital- and spin-driven lattice instabilities above and below $T_s$, respectively, is unique to the orbital-spin zigzag chain system of CaV$_2$O$_4$.
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