Interactions between oil prices and the stock market are complex both in the time and frequency domain. Unlike previous studies mainly focus on the dynamic correlation of specific oil-stock nexus with bivariate model; we explore the co-movement among coherence of oil-stock nexuses from a multivariate perspective with an integrated research framework composed by the wavelet coherence and the complex network. Multiple oil prices of Brent, Dubai, Minas and OPEC (Organization of the Petroleum Exporting Countries) as well as Shanghai Composite index are chosen as data sample. In term of the frequency, coherence of multiple oil prices with the stock market measured via the wavelet coherence is tremendously different in the short time scale, even though integral trends of multiple oil prices in the holistic time domain are highly similar, which means that the multiple oil portfolio could reduce the risk in the short term. Concerning changes over the time, co-movement matrix is defined to reflect that coherence of multiple oil-stock nexuses move in different or similar manner at each time point. We find that the coherence of the stock market with Brent and OPEC move diversely during 80% of the sample period, which indicates that portfolio involving Brent, OPEC and Chinese stock index could improve the diversification. Co-movement matrixes with high betweenness centrality could be considered as clues of unusual market fluctuations. This study offers more information for investors focusing on hedging strategies when investing in Chinese stock market and international crude oil markets.