Energy-based detection and estimation are crucial in sensor networks for sensor localization, target tracking, etc. In this paper, we present novel Gaussian approximations that are applicable to general energy-based source detection and localization problems in sensor networks. Using our approximations, we derive receiver operating characteristics curves and Cramer-Rao bounds, and we provide a factorized variational Bayes approximation to the location and source energy posterior for centralized or decentralized estimation. When the source signal and the sensor noise have uncorrelated Gaussian distributions, we demonstrate that the envelope of the sensor output can be accurately modeled with a multiplicative Gaussian noise model, which results in smaller estimation biases than the other Gaussian models typically used in the literature. We also prove that additive Gaussian noise models result in negatively biased speed estimates under the same signal assumptions, which can be circumvented by the proposed approximations.