Despite accumulated research findings confirming the link of multiword sequences (MWSs) structures and functions to essay quality, as well as the connection between MWSs statistical features (e.g., their frequency and association strengths in BNC/COCA) and writing quality, to date no study integrated these two separate lines of investigations. It remains to investigate whether and how MWSs structures, functions and their statistical features jointly affect writing quality. Drawing on 900 rated argumentative essays composed by Chinese grade 12 students in National Matriculation Test, the present study employed CollGram to automatically identify the nativelike 4-word sequences in these essays and to analyze their frequency and Mutual Information (MI) scores in COCA. The structures and functions of frequent nativelike 4-word sequences were also analyzed manually. A serial of linear mixed-effect models was constructed to investigate their main effects as well as interaction effects on essay scores. The best fit model revealed the links of higher essay scores to higher MI scores, to more noun-phrase sequences, to more stance sequences, as well as to fewer referential sequences. Additionally, the interaction of prepositional phrase sequences and their frequency in COCA affected essay scores, so did the interaction of verb phrase sequences and their MI in COCA, as well as the interaction of noun phrase sequences and their MI in COCA. The findings provide new insights into the complex interaction between MWSs structures, functions and their statistical features, as well as their joint effects on writing quality.