That is lame. I'm pretty sure they still give child support even if he is unemployed it might not be much. But also a judge will evaluate where his $$ is coming from.
What you are going to do is ask that he be imputed income to what he made before he voluntarily left his job. Barring that, he should be imputed minimum wage at full-time hours at the very least.
You may be able to get assistance even though you live with your parents. Where I live, you just have to prove that you buy your own groceries (i.e. I assume with receipts?) So call the local office and see if you can at least be eligible for state insurance, etc. if you need it. Can't hurt to ask!
As for you child support, I don't really have any experience with that situation, but I believe he would have an imputed income based on his previous income. I don't know if his going to school interferes with that. Good luck mama!
Since he will have no record of income, unless you can prove his earnings from the under the table jobs, the amount that he is very likely to be imputed will be 40 hours at minimum wage. You will get a child support order. Doesn't mean that he will pay, but you will have the order. And if he gets a regular job that isn't under the table, the support (along with the arrears) can be garnished from his check.