He cannot if you are required to file a tax return.

If you're not required to file, he could if they lived with him all 12 months of the year and he provided more than 1/2 of their support.  However, as they are not related to him he could claim their exemption and child tax credit, but not Head of Household Status, EIC or the Child and Dependent Care Credit.

I have to file a return due to me having a w2 for a summerr job. He is the pretty much supporting them. So your stating he can not claim them as dependents?

My children have lived with him the the entire year of 2016 and he helps support them 70/30.

You are required to file a return if your gross income was $10,350 or over.  If not, you are not required to file a return, even if you file one to get a refund of tax withheld.