High field electron spin resonance (ESR) and magnetization measurements reveal the crucial role of the strong spin-lattice coupling to generate the peculiar phase transitions in the chromium spinel oxide CdCr2O4, which possesses a spin-driven Jahn-Teller transition and a field-induced 1/2-magnetization plateau state. From our analysis of the ESR modes and the spin wave dispersion, which was observed from the previous neutron scattering studies, these magnetic properties are shown to originate from the modifications of the exchange interactions due to the lattice distortions. The evaluated exchange constants are examined by the magnetoelastic theory proposed by Penc et al.