Can the child support enforcement office help me take him to court to sign over his rights and to have someone else adopt them?

Too many "him" and "them" pronouns to clearly understand.

We need to know the circumstances in order to answer.

I am guessing that there is an open child support order and the father is in arrears. Someone else wants to adopt the children - and that varies by State. You need the father's signature.

No, Child Support cannot and will not help you with this.

Legal Aid might.

No they can not. What your talking about is a custody issue which is separate from support.

No, child enforcement does just that enforce child support orders. Now if they are going after him hard, he may be more willing to do something, but you will have to go to and though court, as noted a local legal aid society may help