Please complete Form 8222, linked below, and mail it to the IRS at the address given in the instructions. The form is "form-fillable", meaning that you can fill in the blanks directly through your computer. The IRS will notify the Social Security Administration of your change of address. If you live in a state with state income taxes, you'll need to also change your address with the Department of Revenue there. Go to your state's DOR website to find out how to change your address there.
https://www.irs.gov/pub/irs-pdf/f8822.pdf
Since the IRS is currently involved in the government shutdown, we can't know how soon the change of address will be officially registered.
As for your W-2 being forwarded by the postal service: I'm not certain that they would forward a tax document. I'd recommend notifying your employer of your change of address so that they can officially change your address. Contact your Human Resources office for assistance.
*** I am NOT a tax expert. I am a seasoned TurboTax user, and volunteer to provide assistance to TT users. Nothing I post is to be considered TAX ADVICE; I bear no legal liability for responses.***
