This paper proposes distributed load shedding policies for regulating excessive network load. Data packets are inserted into the network to be delivered to intended destinations. The intermediate network nodes may decide to forward or shed some packets depending on temporally available resources. It is possible for some packets to traverse several nodes in the network until they are finally dropped before reaching the destination, which exacerbates energy consumption. We define a multi-objective optimization problem where we aim to minimize the used energy subject to providing maximum sum throughput. For the case of single-path unicast sessions, we show that Energy-efficient Distributed Load Shedding (E-DLS), a simple shedding mechanism combined with pushback routing, solves this load di shedding optimization. We implement E-DLS in a testbed and use the experiments to select policy parameter values that strike a good balance between energy and delay performance. We then propose a heuristic extension of E-DLS for multirate multicast routing, and showcase via testbed experiments its optimal performance.