Three-way conflict analysis resolves real-world conflicts in two main steps: identifying the causes of conflict and designing feasible strategies to mitigate disputes. Existing approaches predominantly rely on linear conflict functions, which are insufficient for capturing nuanced variations in inter-agent relationships. Moreover, systematic development of feasible strategies has been limited. To address these limitations, this paper proposes a three-way conflict resolution model incorporating nonlinear conflict functions. Firstly, we introduce nonlinear conflict functions that accurately model the subtle fluctuations in conflict degrees. These functions are used to trisect both the set of agent pairs and the set of issues. We further propose a novel method to determine optimal trisections along with the corresponding optimal threshold pairs. Once the trisection phase is completed, we precisely identify the critical conflict issues that require resolution, where the parameter of conflict tolerance level is induced from the optimal issue trisection. Subsequently, conflict resolution of critical issues is formulated as an optimization problem, and two adjustment mechanisms are developed to derive distinct adjustment strategies. Finally, the applicability and superior performance of the proposed model, in terms of accurately identifying conflict issues and generating effective resolution strategies, are demonstrated through a commonly-used case study, a sensitivity evaluation, and a comparative analysis. The results confirm that our approach offers a flexible, efficient, and practical framework for three-way conflict analysis in complex decision-making contexts.