In this paper, we propose a new distributed energy beamforming and information transfer (DEBIT) scheme for realizing simultaneous wireless information and power transfer (SWIPT) in multiway relay networks (MWRNs), where multiple single-antenna users exchange information via an energy-constrained single-antenna relay node. We investigate the optimal transceiver designs to maximize the achievable sum-rate or the harvested power. The resultant sum-rate maximization problem is non-convex and the global optimal solution can be obtained through a three-dimensional search in combination with conventional convex optimization. To reduce the computation complexity, a suboptimal DEBIT scheme is also proposed, for which the optimization problem becomes linear programming. The achievable sum-rate performance is analyzed and a closed-form lower bound is derived for the MWRN with a large number of users. Furthermore, we consider the harvested-power maximization problem under a target sum-rate constraint, and derive a lower bound of the average harvested power for MWRNs with a large number of users. Numerical results show that the DEBIT scheme significantly outperforms the conventional SWIPT and the derived lower bounds are tight.