There is an increasing demand for intelligent processing on emerging ultra-low-power internet of things (IoT) devices, and recent works have shown substantial efficiency boosts by executing inference tasks directly on the IoT device (node) rather than merely transmitting sensor data. However, the computation and power demands of Deep Neural Network (DNN)-based inference pose significant challenges for nodes in an energy-harvesting wireless sensor network (EH-WSN). Moreover, these tasks often require responses from multiple physically distributed EH sensor nodes, which imposes crucial system optimization challenges in addition to per-node constraints. To address these challenges, we propose \emph{Seeker}, a novel approach to efficiently execute DNN inferences for Human Activity Recognition (HAR) tasks, using both an EH-WSN and a host mobile device. Seeker minimizes communication overheads and maximizes computation at each sensor without violating the quality of service. \emph{Seeker} uses a \emph{store-and-execute} approach to complete a subset of inferences on the EH sensor node, reducing communication with the mobile host. Further, for those inferences unfinished because of harvested energy constraints, it leverages an \emph{activity aware coreset} (AAC) construction to efficiently communicate compact features to the host device where ensemble techniques are used to efficiently finish the inferences. \emph{Seeker} performs HAR with $86.8\%$ accuracy, surpassing the $81.2\%$ accuracy of a state of the art approach. Moreover, by using AAC, it lowers the communication data volume by $8.9\times$.