The recent advancement in deep learning (DL) for automatic modulation classification (AMC) of wireless signals has encouraged numerous possible applications on resource-constrained edge devices. However, developing optimized DL models suitable for edge applications of wireless communications is yet to be studied in depth. In this work, we perform a thorough investigation of optimized convolutional neural networks (CNNs) developed for AMC using the three most commonly used model optimization techniques: a) pruning, b) quantization, and c) knowledge distillation. Furthermore, we have proposed optimized models with the combinations of these techniques to fuse the complementary optimization benefits. The performances of all the proposed methods are evaluated in terms of sparsity, storage compression for network parameters, and the effect on classification accuracy with a reduction in parameters. The experimental results show that the proposed individual and combined optimization techniques are highly effective for developing models with significantly less complexity while maintaining or even improving classification performance compared to the benchmark CNNs.