If I messed up on my taxes a few years back, and I owe the IRS - will they also take the remaining amount from my state refund?

I suspect the IRS will not apply your state refund to your federal tax liability.  Once they process your latest federal tax return, they will issue you a letter stating the amount of tax, penalty, and interest due to resolve your remaining tax liability.  The unpaid tax will continue to be subject to penalty and interest until you make full restitution.

Thank you!