Linear active noise control (ANC) systems have been used in the past to effectively suppress Gaussian noise. A practical ANC system must consider nonlinearities in the secondary path with a non-minimum phase. For an ANC system to effectively operate in a modern-day acoustic environment with multiple electrical/electronic systems operating in the vicinity, the reference noise source is taken as a non-Gaussian stochastic process. Linear systems have shown unacceptable performance in countering the disturbances that are impulsive in nature. Considering these issues, we propose a family of adaptive algorithms for ANC systems that employ a second-order Volterra filter for accurate modeling of the impulsive disturbances. We utilize the maximum correntropy criterion as the cost function to improve the adaptive filtering process, which generates the most appropriate output signal in the ANC system’s successive iterative stages. The proposed algorithms feature dynamic learning-rate parameters, which improve the tracking performance of the algorithms. Also, a careful selection of the Volterra filter’s kernel size in the proposed algorithms ensures a balance between system stability and convergence rate. These parameters are made automatically adjustable, based on the residual error and the reference input signals, to optimize performance in non-Gaussian environments. A comparison of the proposed algorithms with its counterparts is presented through computer simulations in terms of average noise reduction for different levels of impulsive noise. The proposed algorithms are also compared with each other to find the best performing algorithm in a non-Gaussian environment. Achieved results exhibit the effectiveness of the proposed algorithms in their ability to attenuate impulsive noise in comparison with the existing adaptive algorithms for ANC systems. Later, the proposed algorithm has been implemented for speech enhancement, where the noise from the speech sample is identified and removed using an adaptive filter algorithm. Simulations reveal that the devised algorithm can effectively denoise speech signals. Further, in the last part of the paper, the VF-MCCRMC is modified in accordance with the energy of the error signal, and the simulation results demonstrated the improvement in stability and error performance.