[en] Results of room-temperature a-b-plane optical-reflection studies of La_2-xSr_xNiO_4+δ (δ=0.0; x=0, 0.05, 0.10, 0.20, 0.21, and δ=0.085; x=0) are presented and cover the photon energy range 0.005<ω<6 eV. A Kramers-Kronig analysis is used to compute the optical conductivity σ(ω) and energy-loss function Im(-1/var-epsilon(ω)). The doping dependence of the TO and LO a-b-plane phonon modes, anomalous midinfrared absorption (mid-IR band), and interband transitions are discussed. The mid-IR band (band maximum ω_m∼0.5 eV) is found to be similar to that observed in the isostructural materials La_2-xSr_xCuO₄, and is identified with photon-assisted hopping of small polarons. A microscopic theory developed by Reik is used to obtain polaron parameters whose values are compared to those obtained similarly for other small-polaron materials