Chinese character decomposition has been used as a feature to enhance Machine Translation (MT) models, combining radicals into character and word level models. Recent work has investigated ideograph or stroke level embedding. However, questions remain about different decomposition levels of Chinese character representations, radical and strokes, best suited for MT. To investigate the impact of Chinese decomposition embedding in detail, i.e., radical, stroke, and intermediate levels, and how well these decompositions represent the meaning of the original character sequences, we carry out analysis with both automated and human evaluation of MT. Furthermore, we investigate if the combination of decomposed Multiword Expressions (MWEs) can enhance the model learning. MWE integration into MT has seen more than a decade of exploration. However, decomposed MWEs has not previously been explored.