It is very difficult to ship and store oil in the volumes that are relevant to modern economies. We are very much in a situation where some regions are business as usual, some regions can't get oil at any cost, and some regions have so much oil they are stopping production because they don't have any where to store it.

In terms of how this impacts prices, the headline number is usually Brent crude, but there are a number of different "flavors" with various geopolitical factors that influence price[1]. For example, the US market is going to respond differently then the Indian market. The former is a net exporter halfway across the globe from the conflict area, the later gets a substantial portion of their oil through the Strait of Hormuz.

If the conflict carries on for a while things will probably normalize across markets as production and shipping adjust to the new reality. But in the short term you are going to have some folks mildly inconvenienced by slightly higher prices, while other folks might not even be able to fill their tanks.

[]1 https://oilprice.com/oil-price-charts/