The relationship between oil price movements and stock markets during the COVID-19 pandemic and the geopolitical crisis like the ongoing Russian-Ukraine war is yet unexplored extensively. This study therefore examines the return-correlation effects of oil prices on stock markets and their spillover effects in oil-exporting and European countries using daily closing data. After estimating the GARCH process, we employ the static and dynamic Markov Switching model that allow the relationship between oil price and stock market to switch between two regimes coined the COVID-19 and the Russia-Ukraine war periods. The static model shows stock price returns to respond positively and significantly to oil price returns in Italy, Germany and the US during the Covid-19 period while the response is significantly positive only for US in the Russia-Ukraine war period. As regards the volatility spillover, significant spillover is found from stock to oil market for Nigeria, vice versa for Saudi Arabia and bi-directional volatility spillover found for the US, Italy and Germany during the COVID-19 period. The policy implication is that Nigeria and Saudi Arabia should prioritize financial policy and energy policy respectively while US, Italy and Germany should adopt policy coordination to stabilize oil-stock market volatility during low oil price period like the COVID-19 period.