In this paper, we reported our experiments with various strategies to improve code-mixed humour and sarcasm detection. Particularly, we tried three approaches: (i) native sample mixing, (ii) multi-task learning (MTL), and (iii) prompting and instruction finetuning very large multilingual language models (VMLMs). In native sample mixing, we added monolingual task samples to code-mixed training sets. In MTL learning, we relied on native and code-mixed samples of a semantically related task (hate detection in our case). Finally, in our third approach, we evaluated the efficacy of VMLMs via few-shot context prompting and instruction finetuning. Some interesting findings we got are (i) adding native samples improved humor (raising the F1-score up to 6.76%) and sarcasm (raising the F1-score up to 8.64%) detection, (ii) training MLMs in an MTL framework boosted performance for both humour (raising the F1-score up to 10.67%) and sarcasm (increment up to 12.35% in F1-score) detection, and (iii) prompting and instruction finetuning VMLMs couldn't outperform the other approaches. Finally, our ablation studies and error analysis discovered the cases where our model is yet to improve. We provided our code for reproducibility.