This paper considers the crucial problem of event detection and localization with sensor networks, which not only needs to detect occurrences but also to determine the locations of detected events and event source signals. It is highly challenging when taking several unique characteristics of real-world events into consideration, such as simultaneous emergence of multiple events, overlapping events, event heterogeneity and stringent requirement on energy efficiency. Most of existing studies either assume the oversimplified binary detection model or need to collect all sensor readings, incurring high transmission overhead. Inspired by spatially sparse event occurrences within the monitoring area, we propose a compressive sensing based approach called CED, targeting at multiple heterogeneous events that may overlap with each other. With a fully distributed measurement construction process, our approach enables the collection of a sufficient number of measurements for compressive sensing based data recovery. The distinguishing feature of our approach is that it requires no knowledge of, and is adaptive to, the number of occurred events which is changing over time. We have validated the signal attenuation event model through testbed experiments with TelosB motes. Extensive simulation results demonstrate that our approach can achieve high detection rate and localization accuracy while incurring modest transmission overhead.