I have child support income and my kids have survivor benefits, can I still file a tax return and claim them as dependents?

The money you hear about people getting for just filing a tax return claiming kids is dependent on you having some earned income (wages or self employment). Without earned income, you are not eligible for the "refundable" Earned Income Credit or Additional Child Tax Credit.

Child support is neither earned income  or even reportable income.

Social security payments to children.

 If the Social Security (SS) payments. Including SS disability, were under his/her SS number (as they usually are), it does not get reported on your return. If it does need to be reported, it would go on his/her individual return. If that was his/her only income, it does not get reported at all. They do not need to file  tax returns. Child support is not income to you or them.

SS is only taxable & reportable when added to sufficient other income. Social security only  becomes taxable, when his income, including 1/2 his social security, reaches $25,000

 You may still claim him, as a dependent, as long as he is not providing more than 1/2 his own support (including the social security being spent on him). Any part of his SS $ put into savings does not count as support.

Note that the requirement is not that you provide more than 1/2 his support (as it is with non child dependants , but only that he didn't provide 1/2. The child support, you receive from the father is considered your money, for the support test. The support value of the home you provided is the fair market rental value of the home plus utilities & other expenses divided by the number of occupants.

 Here's a good article on the subject:

http://www.fool.com/taxes/2002/taxes020315.htm