Your description is puzzling in that it appears that you have done everything right.
I suppose that someone could have dropped your tax file in the IRS mailroom and the W-4s got separated from your return. If so, then just sending them a copy of the W-2s again with a letter of explanation should be sufficient.
Off hand, I don't know of other forms that easily come to mind on which Social Security taxes are withheld. Social Security taxes are part of the "self-employment" taxes that are calculated on Schedule SE (if you are self-employed) and yes this amount is added to the line 11 Schedule 3 (1040) amount.
And some people are not required to have Social Security withheld. Certain government employers (some federal, state and local governments) don't have to withhold social security tax (because employees pay into a different retirement system).
But this is puzzling. I would just write them back in a timely manner, include the copies of the W-2s, outline in your letter what you are sending and how the sum of the box 4s is more than $8,240, and ask them to explain to you why they are not satisfied with this. I.e., what are you missing?
It just sounds like they don't have the same information as you do.
Bill
P.S. one more thing: are you here on a visa (since you said something about an ITIN for your spouse, it makes me wonder if you are here working in the US on a visa)? Some people on certain visas are not supposed to have any Social Security or Medicare tax withheld - but employers get this wrong all the time. If you don't mind me asking, what sort of visa are you here on?
