I owe more state tax for 2016 than shown on my w-2's--can I deduct this amount on my 2016 federal tax return (itemized deductions) and how do I do that?

No, any additional state tax owed can be claimed as an itemized deduction on your 2017 tax return.  The IRS allows the deduction for the year in which the state/local taxes are actually paid.

Only the 2016 taxes withheld, estimated payments made during the year, and any overpayment carried forward from the previous year's return will be available as a deductible amount on the current return.