We present experimental evidence for the formation of localized Wannier-Sta-rk states in the depletion region of low band-gap InAs/(GaIn)Sb superlattice (SL) infrared photodiodes. In the photocurrent spectra of reverse-biased photodiodes, maxima are observed, that spectrally shift when the strength of the electric field in the depletion region of the diode is changed. Taking into account the spatially indirect type-II nature of interband transitions in InAs/(GaIn)Sb SL's, the spectral positions of the observed maxima can be explained in the framework of localized Wannier-Stark states. Besides photocurrent spectra, the current-voltage (I-V) characteristics of the diodes were investigated. In the reverse-bias regime dominated by Zener tunneling the differential resistance of the diodes reveals an oscillatory behavior. These oscillations are due to a resonant enhancement of the Zener tunneling current by Wannier-Stark states in the depletion region of the SL diode. A model is presented that quantitatively describes the occurrence of the oscillations in the I-V curves. In addition, the influence of a magnetic field on the Wannier-Stark oscillations in the Zener current was investigated. While the period of the oscillations in the I-V curves is conserved, the resonances are shifted, reflecting the energy shift introduced in the Wannier-Stark states by the magnetic field. This voltage shift exhibits a strong dependence on the magnetic-field orientation.