The influences of extreme events on crude oil market is of great significance in crude oil price analysis and the growing Internet concern about emergencies often accompanies panic of the market traders, which would probably result in turmoil and instability of the oil market. In this paper, a novel modeling framework that integrates Bivariate Empirical Mode Decomposition (BEMD) and Autoregressive-Generalized Autoregressive Conditional Heteroskedasticity (AR-GARCH) is proposed for analyzing the effects of three types of oil-related events (abnormal climate, economic crisis, war) on crude oil market. The Internet concern derived by search volumes from Google Trends is introduced to characterize the magnitude and dynamic path of the response to oil-related events. In our approach, the original time series is decomposed into several intrinsic modes with different time scale, capturing the fluctuations caused by extreme events. The empirical results indicate that oil prices responding to different types of oil-related events present differentiation. Meanwhile, the effects of various intrinsic modes are also different, which implies distinguishing conduction ways and effects with different frequencies. By incorporating open source data into BEMD-based event analysis, this paper provides a feasible solution to estimate the impacts of extreme events on crude oil market.