The only legal way to avoid income taxes is to not have any income.
Other than that, unless you are willing to individually have an "all cash" existance, you will get caught.
Telling your employer that you have 20 dependents, will only get you in trouble. So, you can't get away with it if you have a "job." If you are self-employed you have many more options to deduct expenses. However, you better have receipts to back up your expenses.
If you just fail to submit a tax return, the IRS will find you. Unless, you have no bank accounts and pay cash for everything. That is a tough existance.
The IRS takes tax avoidance very serously .