Generally, if you are no longer employed, you are given some options about your 401(k) (depending on the balance in the account). You can elect to receive the money as a distribution, and use it however you need to. This will never qualify as a "hardship" distribution, and hardship distributions are not exempt from the 10% early withdrawl penalty (unless they qualify under some other category, such as Medical).

The other drawback is, they do not have to distribute the money quickly, so it may take months to get it.

See if your state will allow you to set up a payment plan. Some do. Then, if you find another job or get a windfall of cash, you can pay your balance off.

The answers to your questions are:

1. Yes, you may cash out your 401k and use the money however you wish, including to pay back taxes.

2. No, needing to pay a large tax bill does not count as a hardship withdrawal. Therefore if you cash out your 401k, you will owe a 10% penalty plus ordinary income tax on the amount that you cash out.