In this paper, we propose a novel multi-task, multi-link relay semantic communications (MTML-RSC) scheme that enables the destination node to simultaneously perform image reconstruction and classification with one transmission from the source node. In the MTML-RSC scheme, the source node broadcasts a signal using semantic communications, and the relay node forwards the signal to the destination. We analyze the coupling relationship between the two tasks and the two links (source-to-relay and source-to-destination) and design a semantic-focused forward method for the relay node, where it selectively forwards only the semantics of the relevant class while ignoring others. At the destination, the node combines signals from both the source node and the relay node to perform classification, and then uses the classification result to assist in decoding the signal from the relay node for image reconstructing. Experimental results demonstrate that the proposed MTML-RSC scheme achieves significant performance gains, e.g., $1.73$ dB improvement in peak-signal-to-noise ratio (PSNR) for image reconstruction and increasing the accuracy from $64.89\%$ to $70.31\%$ for classification.