This paper proposes a novel framework of resource allocation in intelligent reflecting surface (IRS) aided multi-cell non-orthogonal multiple access (NOMA) networks, where a sum-rate maximization problem is formulated. To address this challenging mixed-integer non-linear problem, we decompose it into an optimization problem (P1) with continuous variables and a matching problem (P2) with integer variables. For the non-convex optimization problem (P1), iterative algorithms are proposed for allocating transmit power, designing reflection matrix, and determining decoding order by invoking relaxation methods such as convex upper bound substitution, successive convex approximation and semidefinite relaxation. For the combinational problem (P2), swap matching-based algorithms are proposed to achieve a two-sided exchange-stable state among users, BSs and subchannels. Numerical results are provided for demonstrating that the sum-rate of the NOMA networks is capable of being enhanced with the aid of the IRS.