Unique electro-optical properties of the oblique helicoidal cholesteric (Ch_{OH}) stem from its heliconical director structure. An applied electric field preserves the single-harmonic modulation of the director while tuning the Ch_{OH} period and the corresponding Bragg-peak wavelength within a broad spectral range. We use the response of Ch_{OH} to the electric field to measure the elastic constants of twist K_{22} and bend K_{33} directly in the cholesteric phase. The temperature dependencies of K_{22} and K_{33} allow us to determine the range of the electric tunability of the Ch_{OH} pitch and the heliconical angle. The data are important for understanding how molecular composition and chirality influence macroscopic elastic properties of the chiral liquid crystals and for the development of Ch_{OH}-based optical devices.