In this paper, an intelligent reflecting surface (IRS)-aided two-way decode-and-forward (DF) relay wireless network is considered, where two users exchange information via IRS and DF relay. To enhance the sum rate performance, three power allocation (PA) strategies are proposed. Firstly, a method of maximizing sum rate (Max-SR) is proposed to jointly optimize the PA factors of user U1, user U2 and relay station (RS). To further improve the sum rate performance, two high-performance schemes, namely maximizing minimum sum rate (Max-Min-SR) and maximizing sum rate with rate constraint (Max-SR-RC), are presented. Simulation results show that the proposed three methods outperform the equal power allocation (EPA) method in terms of sum rate performance. In particular, the highest performance gain achieved by Max-SR-RC method is up to 45.2% over EPA. Furthermore, it is verified that the total power and random shadow variable Xσ have a substantial impact on the sum rate performance.