Does an early withdrawl from a 401k effect my state tax refund, because the state refund is saying we owe, not the federal?

The 401(k) withdrawal would increase your taxable income on your federal return and state return. If you had only federal income tax withheld from it, but none for state income tax, it is very likely you will have a smaller refund or even balance due on your federal and state. 

you owe the state because your state withholding was not enough.

you don't owe the IRS because your withholding was enough.

An early withdrawal from 401k pays an extra 10% federal penalty tax.