This paper investigates the security enhancement of an intelligent reflecting surface (IRS) assisted non-orthogonal multiple access (NOMA) network, where a distributed IRS enabled NOMA transmission framework is proposed to serve users securely in the presence of a passive eavesdropper. Considering that the instantaneous channel state information (CSI) of the eavesdropper is challenging to acquire in practice, we utilize the secrecy outage probability (SOP) as the security metric. A problem by jointly optimizing the transmit power at the base station (BS) and reflection phase shifts at IRSs, subject to the successive interference cancellation (SIC) decoding constraints and SOP constraints, is formulated to maximize the minimum secrecy rate among legitimate users. To tackle the non-convex problem, we first derive the exact SOP in closed-form expressions and then propose a novel ring-penalty based successive convex approximation (SCA) algorithm to design power allocation and phase shifts jointly. Numerical results validate the convergence and the secrecy superiority of proposed scheme over the baseline schemes.