do my children have to pay tax on survivor benefits in ohio

The issue is household income, your income, and who claims the children as exemptions. In your instructions booklet for the 1040EZ, 1040A, or 1040, there is a worksheet that will walk you through the calculations.  More likely than not, the benefits will not be taxable.  However, to be on the safe side, you should take a few minutes and do the math.