When the oil price increases, it not only directly raises the cost of fuel/gas for consumers, but it also raises the costs of all other goods that are transported. These price increases will be passed on to the consumer, giving rise to inflation.
With prices rising, workers (and/or unions) will pressure employers for higher wages to compensate for the increased cost of living. If there is a risk of price increases translating into a spiral of rising producer costs and wages – then central banks is likely to intervene by tightening monetary policy – by for example raising interest rates. The higher interest rates will then act as a “signal” to market participants that “monetary authorities” will not tolerate higher inflation. (Higher interest rates will lower disposable income and suppress demand – therefore making it difficult for firms to pass on price increases and/or agree to “excessive” wage demands).
To come back to your question on the impact on food items, higher energy prices affect production costs (directly through fuel and fertilizers), as well as due to the higher the cost of moving food from the farmgate to the market. Obviously, the effect will be less for commodities with a high value and low weight and vice versa. Estimates suggest that a 10% increase in energy prices is associated with a 2 to 3% increase in the prices of grains and vegetable oils (also see Commodity Annex, P10 http://siteresources.worldbank.org/INTPROSPECTS/Resources/334934-1304428586133/GEP2011bCommodityAppendix.pdf). Note also that over the longer term, high energy prices tend to affect food prices through the biofuel channel.