Centrosymmetric compounds which host three-dimensional topological spin structures comprise a distinct subclass of materials in which multiple-𝐪 magnetic order is stabilized by anisotropy and bond frustration in contrast to the more common path of antisymmetric exchange interactions. Here we investigate static and dynamic magnetic properties of the cubic perovskite SrFeO3—a rare example of a centrosymmetric material hosting two types of topological spin textures: skyrmionlike and hedgehog-lattice phases. Our detailed magnetization and dilatometry measurements describe the domain selection processes and phase transitions in SrFeO3. Spin excitations are investigated using inelastic neutron scattering for all three zero-field phases. In the higher-temperature ordered phases, high-energy magnons increasingly lose coherence, so that spin fluctuations are dominated by a distinct quasielastic component at low energies. We anticipate that this could be generic to symmetric helimagnets in which the chiral symmetry is spontaneously broken by the magnetic order.