My ex husband has stated that he is going to claim my son (his step son) and myself on his tax return. We divorced 9/2016. Is he able to do this?

If you are legally divorced you can't file jointly.

He can't claim you (since you are not related any more) as a spouse.  He can't claim you as a dependent unless you lived in the same household for the entire year, and he paid more than half your living expenses, and you earned less than $4050 of taxable income.

Even if the child is not his biological child, the fact that you were married means he is a stepfather, and that gives him the same ability to claim a dependent child as a biological parent, and the stepparent relationship for tax purposes is not ended by divorce.  So, he can claim the child as a qualifying child dependent if the child lived in his home at least half the year (at least 184 nights).  That might include time before the divorce if you lived together, plus any nights the child lived with him after the divorce.  If you also had custody more than 184 nights of the year, then the parent where the child lived the most number of nights is the parent who can claim the child as a dependent.

If your ex did not have custody or live with the child more than 183 nights, then your ex can't claim the dependent unless you give the ex a signed release form.

However, this is complicated by you working "under the table."  If you don't report taxable income and don't file a tax return, then your ex is the only "taxpayer" who might qualify to claim the child as a dependent.