We study parametric instability of compact axion dark matter structures decaying to radiophotons. Corresponding objects - Bose (axion) stars, their clusters, and clouds of diffuse axions - form abundantly in the postinflationary Peccei-Quinn scenario. We develop general description of parametric resonance incorporating finite-volume effects, backreaction, axion velocities, and their (in)coherence. With additional coarse graining, our formalism reproduces kinetic equation for virialized axions interacting with photons. We derive conditions for the parametric instability in each of the above objects, as well as in collapsing axion stars, evaluate photon resonance modes and their growth exponents. As a by-product, we calculate stimulated emission of Bose stars and diffuse axions, arguing that the former can give larger contribution into the radio background. In the case of QCD axions, the Bose stars glow and collapsing stars radioburst if the axion-photon coupling exceeds the original Kim-Shifman-Vainshtein-Zakharov value by 2 orders of magnitude. The latter constraint is alleviated for several nearby axion stars in resonance and absent for axionlike particles. Our results show that the parametric effect may reveal itself in observations, from fast radio bursts to excess radio background.