Determination of the hyperfine-interaction parameters, acoustic and elastic properties of the high-entropy Al$_{x}$CuCrCoNiFe alloys (HEAs) ($x$ = 1, 1.8) in the as-cast state is carried out with the use of Mössbauer spectroscopy, x-ray diffractometry and high-precision ultrasonic techniques. Wide distributions of both the hyperfine-magnetic fields on iron nuclei (5.0–36.3 T) and the isomer shifts (-0.15–+0.28 mm/s) are detected in the HEAs that is result of multiphase state and inhomogeneous short-range order in the phases. As shown, the as-cast Al$_{x}$CuCrCoNiFe HEAs are acoustically and elastically inhomogeneous systems. Mean elastic moduli of the as-cast equimolar HEAs ($\langle E\rangle$ = 172.8 GPa, $\langle G\rangle$ = 65.3 GPa, $\langle B\rangle$ = 161.8 GPa) and the Debye temperature ($\langle\Theta_{D}\rangle$ = 436 K) exceed ones for the elemental metals composing HEAs. There are the Poisson’s ratio $\langle\eta\rangle$ = 0.312–0.322 and the ratio $\langle B\rangle$/$\langle G\rangle$ = 2.321–2.477. Deviation from equimolar content of Al ($x$ = 1.8) results in redistribution of the spin and charge s-electron densities near iron nuclei, increases the elastic moduli and the Debye temperature by approximately 4–5%.