I owe back child support in California. Can they take my federal tax return or my federal stimulas package return?

You can check in advance if you are flagged for offset or not by calling FMS Autoresponder line at 1-800-304-3107.

Yes they may take it, if they have filed to garnish it.

I received child support for back taxes, but my ex filed some kind of form with the IRS to have his taxes returned to him. Now they are asking me to pay his taxes back, how can this happen? He pays only 60 to 150 sporadicly for three children.

You need to challenge his rebuttal. Assuming you followed proper channels to get the tax refund confiscated to begin with, you have the right to challenge any rebutal he may have filed.