We present a new way of deriving effective theories of dynamical electromagnetic fields in general media. It can be used to give a systematic formulation of magnetohydrodynamics (MHD) with strong magnetic fields, including systems with chiral matter and Adler-Bell-Jackiw (ABJ) anomaly. We work in the regime in which velocity and temperature fluctuations can be neglected. The resulting chiral anomalous MHD incorporates and generalizes the chiral magnetic effect, the chiral separation effect, the chiral electric separation effect, as well as recently derived strong-field MHD, all in a single coherent framework. At linearized level, the theory predicts that the chiral magnetic wave does not survive dynamical electromagnetic fields. A different chiral wave, to which we refer as the chiral magnetic electric separation wave, emerges as a result of dynamical versions of the chiral electric separation effect and the chiral magnetic effect. We predict its wave velocity. We also introduce a simple, but solvable nonlinear model to explore the fate of the chiral instability.