If you pay the money back in 2018 and they adjust your W-2, then no further tax deduction or adjustment is needed, the money was already removed from your taxable wages. Scroll down to part 2.
Part 1. Tax adjustments.
If you repaid the money and it is not reflected on your W-2 (or you quit in 2017 and repaid in 2018), then you have two ways to deduct the repayment from your taxes.
A. You can take a special itemized deduction not subject to the 2% rule. This is found in the "Other Uncommon Deductions" section.
B. You can take a special tax credit called a "claim of right" credit. Basically, you refigure your income taxes for each year covered by the repayment and calculate what your taxes would have been if you hadn't received the income you had to repay (how much less tax you would have paid.) Add up those amounts and take a direct tax credit on the tax return. This requires using Turbotax desktop version installed on your own computer from a CD or download so you can manually enter the credit in Forms mode. Turbotax also doesn't calculate the credit for you, you have to do it yourself, or see a professional.
Generally, if your income and tax brackets are about the same, and you already itemize your deductions, the two methods result in the same tax savings. However, because the tax rate is dropping for 2018, if you make the repayment in 2018, the claim of right method will probably lower your taxes more than the itemized deduction.
Here is a link to further instructions for the claim of right procedure. https://ttlc.intuit.com/questions/2993187-claim-of-right-over-3-000-where-do-i-enter-in-turbo-deluxe
Also note that if you use the itemized deduction procedure, the deduction will probably transfer to your state tax return automatically so you get a state tax deduction. If you use the claim of right procedure, you won't get a state tax deduction or credit automatically, you will have to investigate whether your state has a claim of right procedure.
And finally, there is no way to get your social security tax back, it's just gone. But the higher income stays recorded on your account which may increase your retirement credits.
Part 2. College tuition
Because you now will have paid for college with your own taxable funds, you are eligible for any tuition credits you qualify for. But, you can't claim them now (unless you had 2017 expenses, which you can claim in 2017), you have to file an amended tax return for each past year to claim any credits for those years. And you can only amend your 2014, 2015 and 2016 returns, it is too late to amend older returns. If you paid education expenses in those years, the amending instructions are attached below.
Likewise, if the company gave you tax free money for moving and you now have to pay it back, that means your moving expenses are paid for with taxable funds and are eligible for the moving expense deduction. But it sounds like you moved more than 3 years ago so the amending deadline is probably passed to actually claim that deduction.
https://ttlc.intuit.com/replies/3288565
