I have to file 2017 state tax with West Virginia and Virginia. Could Turbotax help me with this issue?

As for doing your 2017 return, you can do it with TurboTax, but you will have to use the desktop software that you will download to your computer - the Online system is only for the current tax year (2019).

For instructions on how to do this, please see this TurboTax FAQ on how to file a prior year return.

If you did not do your 2017 federal return in TurboTax, you will have to enter all your federal data and then do the state returns.

I haven't filed return for the years 2017 and 2016. for both federal and VA state taxes.  Can turboTAX software do both ?

Not with the Online software...that's only for 2019 right now.

You buy/download and install the separate 2017 & 2016 software onto your full MAC or Windows computer.......prepare each year separately, and mail the forms in to the IRS and VA.  Each year mailed in separate envelopes too.

https://turbotax.intuit.com/personal-taxes/past-years-products/2017