We present multiwavelength observations of the interstellar medium in the disturbed galaxy NGC 4438. We find extended emission-line filaments, which are kinematically unrelated to the galaxy disk. For one of these features, an extended loop, we propose a scheme in which the 'bubble' seen at radio wavelengths has swept a clear path for outflowing material from the nucleus to ionize more distant material. Another radial emission-line feature might represent shocks in the disk along a gravitationally-defined caustic produced during a tidal encounter, or a 'searchlight beam' escaping the inner dusty regions of the galaxy. Energy-balance arguments favor the shock picture, but further study will be important in understanding this feature. Emission-line ratios indicate that shocks may be important in the energetics of the interstellar medium (ISM) through much of the disk of NGC 4438; the alternative is star formation in a uniformly very dense ISM. We use K-band data to locate the stellar peak of the galaxy, which is just outside the prominent radio-continuum loop or shell feature. The nucleus itself is at most a very weak radio source. However, the more extended radio structure shows that energetic events have taken place in the innermost few hundred parsees of NGC 4438. The interstellar medium of NGC 4438 may show at once the impact of nuclear energy input (from an AGN or cocooned starburst), perturbation by the companion NGC 4435, and interaction with the dense intergalactic medium in the Virgo core.