With excellent energy resolution and ultralow-level radiogenic backgrounds, the high-purity germanium detectors in the Majorana Demonstrator enable searches for several classes of exotic dark matter (DM) models. In this work, we report new experimental limits on keV-scale sterile neutrino DM via the transition magnetic moment from conversion to active neutrinos ν_{s}→ν_{a}. We report new limits on fermionic dark matter absorption (χ+A→ν+A) and sub-GeV DM-nucleus 3→2 scattering (χ+χ+A→ϕ+A), and new exclusion limits for bosonic dark matter (axionlike particles and dark photons). These searches utilize the (1-100)-keV low-energy region of a 37.5-kg y exposure collected by the Demonstrator between May 2016 and November 2019 using a set of ^{76}Ge-enriched detectors whose surface exposure time was carefully controlled, resulting in extremely low levels of cosmogenic activation.