I am a postdoc (married, J-1, foreigner). How can I refund my federal tax while my wife (J-2) does not have a SSN/ITIN? Thanks a lot.

If by federal taxes you are referring to U.S. Social Security and Medicare taxes - then yes, a J-1 visa holder is exempted from the requirement to pay Social Security and Medicare; you can pursue obtaining a refund of improperly withheld Social Security and Medicare taxes via two routes:  

1. You can request that your employer refund the withheld taxes to you.  
2. If the company will not refund the withheld taxes to you, you can file a claim for refund with the Internal Revenue Service on Form 843, Claim for Refund and Request for Abatement.

For more information, see the folllowing IRS guide on Social Security Tax / Medicare Tax and Self-Employment:

https://www.irs.gov/individuals/international-taxpayers/social-security-tax-medicare-tax-and-self-em...

Please note that J-1 visa holders who substantially comply with the requirements of that visa, and who do not exceed the duration of their specific Visitor Exchange Program, are exempt from the Substantial Presence Test used to determine eligibility for being a resident alien for U.S. income tax purposes: this means that you are considered a nonresident alien.

As a nonresident alien you will need to file a Form 1040NR to report any U.S.-source income you have. TurboTax does not support Form 1040NR, so you will not be able to use TurboTax for your specific tax situation.

You may want to check out Sprintax, who are specifically geared towards nonresident aliens with 1040NR filing requirements.

For more information please see IRS Publication 519, US Tax Guide for Aliens:

https://www.irs.gov/pub/irs-pdf/p519.pdf