Can an employee work you and never have you fill out any type of paperwork for employment?? Also, pay you without withholding any taxed?

Your employer must withhold taxes from your pay - income tax, social security, and medicare - unless you're a contractor and not a true employee. At the end of the year the employer must provide a W2 form that documents your pay and taxes withheld, and for contractors they must provide a 1099 form.

When you first start work your employer must have you fill out a W4 form, so that they can withhodl the proper amount of tax. They should also request you to provide proof of citizenship status. If they aren't doing any of this they are liable for big penalties from the IRS - again, assuming you are a true employee and not an independent contractor.

It's called "working under the table" and it's illegal. Some people like to work that way so that they don't have to pay taxes. Every year they don't pay in to Social Security, for example, lowers the amount that they will get in their monthly SS checks, when they retire. It's not a smart thing to do.
Your boss is screwing you over, for your retirement later on. I would turn him in to the IRS.

What Chrissy says is accurate.

However, her advice is also a good way to find yourself unemployed, because your boss WILL figure who turned him into the IRS.

If you want to tell us more, please do so. Some employers illegally pay cash under the table short term and you have to decide if you want to take the risk of no workmen's comp etc. Some pay you flat rate and give you a 1099 at the end of the year and YOU have to pay higher taxes on that income than if you had regular wages. That may or may not be illegal, depending on the situation.
As stated, you also have to decide how much you want the work, but I would at least find out if a 1099 is going to be filed, and answer back.