In this paper we present an intrusion-resilient distributed algorithmic approach to estimate the electro-mechanical oscillation modes of a large power system using Synchrophasor measurements. For this, we first show how to distribute the centralized Prony method over a network consisting of several computational areas using a distributed variant of alternating direction method of multipliers (D-ADMM). We then add a cross-verification step to show the resiliency of this algorithm against the cyber-attacks that may happen in the form of data manipulation. We illustrate the robustness of our method in face of intrusion for a case study on IEEE 68-bus power system.