No, you can't get your 2016, 2017 and 2018 W-2's from TurboTax. However, you may be able to get 2016 and 2017 W-2's from the IRS by getting an online wage and income transcript.
Additional information: Is it still possible to e-file 2017, 2016, or earlier tax returns in TurboTax?
The Wage and Income Transcript, though, will not include State info. Check with your employer(s).
OP can also get actual W-2 forms from the Social Security Admin, but there is a charge.
<a rel="nofollow" target="_blank" href="https://faq.ssa.gov/en-us/Topic/article/KA-02501">https://faq.ssa.gov/en-us/Topic/article/KA-02501</a>