Manipulating interest rates is one of the things that the Federal Rreserve does to carry out montery policy. The Fed changes interest rates to try to prevent excessive inflation or to try to give the economy a boost. When the Fed raises interest rates, it is generally trying to prevent inflation. That tells us that raising interest rates will tend to decrease the prices of most goods and services.
When interest rates go up, it is harder for people (and businesses) to borrow. If people borrow less, they will be less able to spend because they have less money. If people in general start to spend less money, that means that aggregate demand will go down. As aggregate demand goes down, the general price level goes down. Therefore, an increase in interest rates is likely to lead to a decrease in the prices of the goods that you mention.
The central bank has overwhelming influence over the United States economy. Their control over interest rate fluctuation has a huge effect over how virtually every business conducts themselves (to say nothing of the consumers). That said, in short, interest rates are like a pressure valve for the economy. For example, in your question, if the fed were to raise interest rates it will change the prices of all three markets that you have listed. First, the housing market will slow down. If the interest rate is raised, this will discourage people from taking out new loans for new homes (it will by definition cost them more). Therefore, we could expect other subsquent changes to related markets, like construction or the lumber industry. For the other two industries, food and oil, you could also see a negative impact over the long run. Businesses, just like people, take out loans from banks to help run their business. With a higher interest rate on tap; farms will be less inclined to take out new loans... less likely to purchase more land, plant more crops... then the laws of supply and demand will swing into action... a lower food supply will invariably lead to a higher food price. With oil, you could expect the same effect... drilling oil takes money... again with a steeper interest rate, oil companies will be less inclined to take out new loans to operate.