Do I have to wait for my W2-C before filing my taxes this year (2020) due to the OASDI payroll tax deferment Executive Order?

[SteamTrain]

Apparently not.  (with a qualification for a certain multiple employers situation ) 

IF you had only one employer during 2020, and the only change will be in box 4, showing that the repayment was done, then no wait is needed, nor is an amended tax return required if you filed earlier (assuming that is the only change, or the change was in box 14 for those railroad employees who pay Tier 1 RRTA tax).

Now, if you had more than one employer during 2020, you might have to either file an extension and wait, or file earlier and amend several months later when you get the W-2C....IF...if the final corrected total for box 4 (or box 14 Tier 1 RRTA tax) from all your employers exceeds 8537.40 because you are due a refund of the amount that exceeds that $$ amount.  This will only happen if your total W-2 wages exceed137,700 for 2020.

Form W-2 Reporting of Employee Social Security Tax Deferred under Notice 2020-65 | Internal Revenue ...

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"Instructions for Employees

If you had only one employer during 2020 and your Form W-2c, Corrected Wages and Tax Statement, for 2020 only shows a correction to box 4 (or to box 14 for employees who pay RRTA tax) to account for employee Social Security (or Tier 1 RRTA tax) that was deferred in 2020 and withheld in 2021 pursuant to Notice 2020-65, no further steps are required. However, if you had two or more employers in 2020 and your Form W-2c for 2020 shows a correction to box 4 (or to box 14 for employees who pay RRTA tax) to account for employee Social Security (or Tier 1 RRTA tax) that was deferred in 2020 and withheld in 2021, you should use the amount of Social Security tax (or Tier 1 RRTA tax) withheld reported on the Form W-2c to determine whether you had excess Social Security tax (or Tier 1 RRTA tax) on wages (or compensation) paid in 2020.

If the corrected amount in box 4 of the Form W-2c for 2020 causes the total amount of employee Social Security tax (or equivalent portion of the Tier 1 RRTA tax) withheld by all of your employers to exceed the maximum amount ($8,537.40) of tax that you owe, or increases an already existing excess amount of employee Social Security tax (or Tier 1 RRTA tax withheld), then you should file Form 1040-X, Amended U.S. Individual Income Tax Return, to claim a credit for the excess Social Security tax (or Tier 1 RRTA tax) withheld. See the instructions to line 10 of Schedule 3 in the 2020 Instructions for Form 1040 and Form 1040-SR for more information."

[SteamTrain]

The payback period has been updated and extended to 31 Dec 2021 instead of 30 April 2021, but as-of 3 Jan, the IRS has not posted news/guidance yet on either the payback period, nor on issuing W-2C forms after payback has been satisfied.  (at least not that I have found yet...but maybe it's buried somewhere)

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DFAS has updated their guidance and procedures for military personnel, Reserve and Guardsmen, and civilian employees:

https://www.dfas.mil/taxes/social-security-deferral/

Text as follows  (in case they move it):

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"UPDATE:  The Consolidated Appropriations Act, 2021 was passed and extended the period for collecting deferred 2020 Social Security taxes.  The period for collection is now January 1, 2021 through December 31, 2021 (instead of January 1, 2021 to April 30, 2021). 
 
At the end of December, the 2020 Social Security tax deferral will end. Beginning January 2021, the normal 6.2% Social Security tax withholdings will again be deducted from pay for military members and civilians, and an additional deduction for the deferred 2020 Social Security tax collection taken from pay.

Per IRS guidance (as modified by the Consolidated Appropriations Act, 2021), the Social Security taxes deferred in 2020 will be collected from pay between January 1 and December 31, 2021.

Military Members -
For active duty military members, the 2020 deferred Social Security taxes will be collected in 24 installments, from your mid-month and end-of-month pay between January 1 and December 30, 2021.

For reservists and guardsmen performing intermittent duty in 2021, the amount collected may not be the same every pay period. DFAS will collect 2% of net available from each weekly, mid-month and end-of-month pay, and will continue until the deferred taxes have been repaid in full.

Beginning in January 2021, your myPay LES will reflect the monthly collection amount and contain a note in the remarks section that shows the remaining balance of deferred Social Security taxes.

Civilian Employees –
The amount of Social Security taxes deferred in 2020 will be collected in 24 installments between pay-periods ending January 16 and December 4, 2021.

Beginning in January 2021, your myPay LES Remarks section will include the 2020 deferred OASDI collection amount in that pay period, as well as the remaining balance to be collected.

If you separate or retire prior to the deferred Social Security tax being collected in full the unpaid balance will either be collected from your final pay or you may receive a debt letter with instructions for repayment.

Background
Pursuant to IRS Notice 2020-65 and at the direction of the Office of Management and Budget and Office of Personnel Management, Social Security (Old Age, Survivors, and Disability Insurance) or “OASDI” tax withholdings were temporarily deferred from September through December 2020 and will be collected from wages paid between January 1, 2021 and December 31, 2021, for employees who had wages subject to OASDI of less than $4,000 in any given pay period.  These actions were in response to the Presidential Memorandum issued on August 8, 2020. "