My sister and her husband have separated and they have two little boys which they gave to me and my husband in August 2012. Neither one wants them and barely have any contact if any at all and no financial help has been given to us. Can I file child abandonment on them?

I think you should have them in court for a number of issues, not just abandonment but custody and child support, but a consultation with any attorney, is a good first step as to what you can do in your state or county. Local laws vary.

No you can't file abandonment. Abandonment is not somehing you can charge someone with or file for.

What you can do is file for full custody or even adoption. You can use abandonment as grounds for getting full custody. But what you want is to get legal custody of the children.