The child tax credit ($2000 per qualifying child under age 17) offsets the tax on up to $20,000 of income. So with the standard deduction for HOH, plus 2 children who both qualify for the tax credit, you would owe no federal tax and expect a refund, so it is normal that no tax is being withheld. The state is probably the same, although I don't know what state or what the tax rates and credits are.
Withholding looks at your paycheck (weekly, biweekly, or whatever) and does a mini-calculation, if this was your income all year, and you have the deductions and dependents you say on your W-4, what would your tax be, and then divides by 52 or 26 or whatever to get the withholding. So in a week that you earn a lot, you will have more taken out and in a week you earn less, less is taken out. From your question (and assuming no other undisclosed factors) you won't owe tax, so there is no withholding.
If the situation changes, like you get a second job, you have to look at the W-4 worksheet and fill out new W-4s for all your jobs at the same time so that your new situation is accounted for.
