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 eavesdropper's instantaneous channel state information (CSI) is challenging to acquire in practice, we utilize secrecy outage probability (SOP) as the security metric. A problem of maximizing the minimum secrecy rate among users, subject to the successive interference cancellation (SIC) decoding constraints and SOP constraints, by jointly optimizing transmit beamforming at the BS and phase shifts of IRSs, is formulated. For special case with a single-antenna BS, we derive the exact closed-form SOP expressions and propose a novel ring-penalty based successive convex approximation (SCA) algorithm to design power allocation and phase shifts jointly. While for the more general and challenging case with a multi-antenna BS, we adopt the Bernstein-type inequality to approximate the SOP constraints by a deterministic convex form. To proceed, an efficient alternating optimization (AO) algorithm is developed to solve the considered problem. Numerical results validate the advantages of the proposed algorithms over the baseline schemes. Particularly, two interesting phenomena on distributed IRS deployment are revealed: 1) the secrecy rate peak is achieved only when distributed IRSs share the reflecting elements equally; and 2) the distributed IRS deployment does not always outperform the centralized IRS deployment, due to the tradeoff between the number of IRSs and the reflecting elements equipped at each IRS.