There may be limited deductions. This is because, when you have a permanent work place, your tax home is the general area of that work place. Since this is the case, your tax home is not South Carolina but the DC area, and specifically Virginia. Please note this IRS link about this subject: Tax Home
Because your tax home is Virginia, you may be required to file a Virginia Resident return. You state you are maintaining a residence there (you are renting). If you are physically present in Virginia for at least 183 days, you are considered an actual resident of Virginia and must file a Virginia resident return (all of your income is taxed in Virginia).
You wouldn't be able to claim the travel between South Carolina to Virginia. Since your tax home is Virginia, this travel is actually considered a personal nondeductible expense. However, if you have a main location you are working from in Virginia, the other temporary locations would be deductions on Form 2106. (The reference I provide above dives into this subject in more detail)
As far as other state returns are concerned, you can simplify things in the future by stating you are a Virginia resident, and having your locations only withhold Virginia tax. Both Maryland and DC have reciprocal arrangements with Virginia, and you would only have to pay tax in Virginia.
However, to not overly complicate things, let me know if any of the jobs were withholding to SC. If not, I'll assist you with your remaining portions of the state returns.
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