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We amalgamate two fundamental designs from distinct areas of wave control in physics, and place them in the setting of elasticity. Graded elastic metasurfaces, so-called metawedges, are combined with the now classical Su-Schrieffer-Heeger (SSH) model from the field of topological insulators. The resulting structures form one-dimensional graded-SSH metawedges that support multiple, simultaneous, topologically protected edge states. These robust, enhanced localized modes are leveraged for applications in elastic energy harvesting using the piezoelectric effect. The designs we develop are first motivated by applying the SSH model to mass-loaded Kirchhoff-Love thin elastic plates. We then extend these ideas to using graded resonant rods, and create SSH models, coupled to elastic beams and full elastic half-spaces.