We investigated moderate-temperature oxygen diffusion mechanisms in Sr₂ScGaO₅ with Brownmillerite structure type. From oxygen isotope ¹⁸O-¹⁶O exchange experiments we determined that oxygen mobility sets in above 550 °C. Temperature-dependent neutron and X-ray (synchrotron) diffraction experiments allowed us to correlate the oxygen mobility with a subtle phase transition of the orthorhombic room-temperature structure with I2mb space group toward Imma, going along with a disorder of the (GaO₄)_∞-tetrahedral chains. From lattice dynamical simulations we could clearly evidence that dynamic switching of the (GaO₄)_∞-tetrahedral chains from its R to L configuration sets in at 600 °C, thus correlating oxygen diffusion with the dynamic disorder. Oxygen ion diffusion pathways are thus constrained along the one-dimensional oxygen vacancy channels, which is a different diffusion mechanism compared to that of the isostructural CaFeO_2.5, where diffusion of the apical oxygen atoms into the vacant lattice sites are equally involved in the diffusion pathway. The proposed ordered room-temperature structure in I2mb is strongly supported by ¹⁷O, ⁴⁵Sc, and ⁷¹Ga NMR measurements, which indicate the presence of crystallographically unique sites and the absence of local disordering effects below the phase transition. The electric field gradient tensor components measured at the nuclear sites are found to be in excellent agreement with calculated values using the WIEN2k program. The oxygen site assignment has been independently confirmed by ¹⁷O{⁴⁵Sc} transfer of adiabatic populations double-resonance experiments.