We investigate the joint and bivariate return and volatility interdependence between various agricultural commodities and oil price shocks. As an alternative of the Diebold and Yilmaz (2012 and 2014) spillover methodology, this paper proposes the application of the fresh time-varying parameter vector autoregression (TVP-VAR) methodology by Antonakakis and Gabauer (2017) during the sample period between January 7, 2000 and September 17, 2020. In addition, this paper pays special attention to the most relevant periods of economic turbulence among the last 20 years: dotcom bubble, Global Financial Crisis (GFC) and COVID-19 pandemic crisis. About the main results, the directional return and volatility connectedness of oil risk shocks is higher than oil demand shocks and, in turn, higher than oil supply shocks. In addition, the dynamic total return and volatility connectedness changes over time, rising during periods of economic crisis. In general, the net return connectedness considerably increases during the three most important crises. Thus, the differences between transmitters' (Canola and Corn) and receivers’ (Orange Juice, Lean Hog, Sugar and Rubber) agricultural commodity markets are emphasized during the GFC and the COVID-19 pandemic crisis. Finally, the net volatility connectedness measure would not show evidence as clear as the net return connectedness measure.