Can a stepdad claim his stepkids for tax credits if they receive social security survivors benefits that are paid to the mother? Biological father is deceased.

The child's Social Security benefits reported on a SSA-1099 should have the child's Social Security number in box 2 of the form.  The child's SS benefits are not reported on the parent's tax return.  If the child has no other income they do not have to file a tax return for the benefits received.

You can claim the step-children as dependents on your tax return just like if they were your biological children.  The Child Tax Credit, EITC , Child and Dependent Care Credit are available if you and the children are eligible.