The money that you took out, should be looked at just like income, like you worked a job and that was your pay check, the tax money is held out just like working a job. I would have thought they would have held out the 10 percent penalty and also state taxes before sending you the balance.
When you file your taxes, this money from the fund along with your other income will be shown as income. You will then list what taxes you paid,
( also since you most likeley did not pay any estimated tax or social security tax on your self employment)
You may either (owe additional tax if they did not hold out enough)
or get some back if they held out more than needed with your other deductions.
If you had any unemployment money, that is also income and has to be reported.
The money from your self employment will be taxed, but if they held out enough from the 401K withdrawer it may or may not cover it.
If they did not withhold any state income tax and your state has a state income tax, you will owe that on both the 401 K money and your self employment income.
If you did not already send in estimated tax on your self employment, you may also owe social security taxes on your self employment money.
And if they did not hold out the 10 percent penalty for the withdraw you will owe it also.
All you can do is get your taxes done by a professional and see what happens, the most important thing is to do them, if you owe money and can't pay, go ahead and still file, there are forms to use to file if you can't pay. You will get into more trouble for not filing than you do for not paying.