The lack of gold standard methodology for synergy quantification of anticancer drugs warrants the consideration of different synergy metrics to develop efficient Artificial Intelligence-based predictive methods. Furthermore, neglecting combination sensitivity in synergy prediction may lead to biased synergistic combinations that are inefficient in conferring anticancer activity. To address this, we proposed a deep learning model, namely SynPredict, which can effectively predict synergy scores in Loewe, zero interaction potency (ZIP), Bliss, highest single agent (HSA), synergy score (S), and combination sensitivity score (CSS). SynPredict explored and assessed the multimodal fusion level of input data, including the gene expression data of cancer cells, along with the representative chemical features of drugs in pairwise combos. SynPredict variants predicted synergy and CSS scores employing the most comprehensive ONEIL and ALMANAC anticancer combination datasets to explore the effect of the data source in model performance in both intermediate and early fusion architectures of the heterogeneous input data. The empirical outcomes revealed that SynPredict outperformed the compelling DrugComb model in Bliss, HSA and ZIP synergy, with a 45-74% decline in the mean square error (MSE). Additionally, it surpassed DeepSynergy, AuDNN synergy and TranSynergy Loewe score prediction models with a 21-34% reduction in MSE. The impact of the utilised data source was found to be more significant and consistent across most synergy models compared to input data fusion architectures. Our findings demonstrated that rapid and less exhaustive in-silico predictions of drug combinations should consider a multiplex of synergy metrics and the combined sensitivity. Moreover, the utilised dataset for model development significantly impacts the subsequent performance of the model.