Electric corona discharge in a multi-phase system results in complex electro-hydrodynamic phenomena. We observed unconventional shock wave propagation on an oil thin film sprayed over a polymer-coated conductor. A hair-thin single shock wave arose when the high voltage bias of an overhung steel needle was abruptly removed. However, such solitary waves possess neither interference nor reflection properties commonly known for ordinary waves, and also differ from the solitons in a canal or an optical fiber. We also observed time-retarded movement for dispersed oil droplets at various distances from the epicenter which have no physical contact, as if a wave propagating on a continuous medium. Such a causality phenomenon for noncontact droplets to move resembling wave propagation could not be possibly described by the conventional surface wave equation. Our systematic studies reveal a mechanism involving oil surface charges driven by reminiscent electric fields in the air when the needle bias is suddenly removed.