Radio frequency spectrum awareness requires the ability to detect, localize, and characterize emitters in dense and contested wireless environments. In this work, we propose a task-oriented distributed compression framework for joint multi-emitter localization and characterization using spatially distributed receivers. Each receiver observes a short window of complex IQ samples, converts the observation to a time--frequency representation, and encodes it into a compact latent vector. A central fusion decoder combines the receiver latents to estimate an unordered set of active emitters, including their locations, center-frequency offsets, occupied bandwidths, and waveform families. A permutation-invariant training objective is used to handle the arbitrary ordering of emitters and predictions. Experiments on synthetic multi-emitter scenes with spectral overlap show that even extremely compact receiver-side representations can preserve useful information for emitter counting and waveform-family estimation. However, accurate localization and spectral-parameter regression require larger latent dimensions. Increasing the receiver latent dimension from $d_{\mathrm{rx}}=1$ to $d_{\mathrm{rx}}=16$ provides the largest improvement, while further increasing to $d_{\mathrm{rx}}=64$ gives smaller gains. These results demonstrate the potential of learned task-oriented compression for communication-efficient distributed spectrum awareness.