In this paper, we analyze the timeliness of a multi-user system in terms of the age of information (AoI) and the corresponding stability region in which the packet rates of users lead to finite queue lengths. Specifically, we consider a hybrid OFDMA-NOMA system where the users are partitioned into several groups. While users in each group share the same resource block using non-orthogonal multiple access (NOMA), different groups access the fading channel using orthogonal frequency division multiple access (OFDMA). For this system, we consider three decoding schemes at the service terminals: interfering decoding, which treats signals from other users as interference; serial interference cancellation, which removes signals from other users once they have been decoded; and the enhanced SIC strategy, where the receiver attempts to decode for another user if decoding for a previous user fails. We present the average AoI for each of the three decoding schemes in closed form. Under the constraint of the stable region, we find the minimum AoI of each decoding scheme efficiently. The numerical results show that by optionally choosing the decoding scheme and transmission rate, the hybrid OFDMA-NOMA outperforms conventional OFDMA in terms of both system timeliness and stability.