Most home furnaces are designed specifically to use heating oil, although some models can handle other fuels. Heating oil is essentially the same as diesel, so diesel can be safely used in oil-burning furnaces and boilers.
While diesel fuel might be easier to find in some places, road maintenance in the United States is largely funded through fuel taxes, which drive up the prices of diesel. Heating oil tends to be significantly cheaper than diesel fuel, and it's often dyed to prevent truck drivers from using it to avoid road taxes. Some furnaces are designed to burn waste oil, but they typically cost significantly more than standard furnaces and might not operate as efficiently.