The olfactory system comprises intricate networks of interconnected brain regions that process information across both the local and long-range circuits to extract odorant identity. Similar to pattern recognition in other sensory domains, such as the visual system, recognizing odorant identity likely depends on highly nonlinear interactions between these recurrently connected nodes. In this study, we investigate whether odorant identity can be distinguished through nonlinear interactions in the local field potentials of the olfactory bulb and telencephalic regions (the ventral nucleus of the ventral telencephalon and the dorsal posterior zone of the telencephalon) in anesthetized rainbow trout. Our results show that odorant identity modulates complex information-theoretic measures, specifically information sharing and redundancy across these brain areas, indicating nonlinear processing. In contrast, traditional linear connectivity measures, such as coherence and phase synchrony, showed little or no significant modulation by odorants. These findings suggest that nonlinear interactions encoded by olfactory oscillations carry crucial odor information across the teleost olfactory system, offering insights into the broader role of nonlinear dynamics in sensory processing.