There is no reciprocal agreement between any of the states you listed. This means:
SC gets a nonresident tax return with the SC wages from working in SC only. SC will not tax the SC source income that was earned in MO.
NC gets a part-year return that will include the SC wages and a SC tax credit plus NC is entitled to a portion of the MO income earned while living there.
MO as a part year resident, you want to file as a resident in order to claim the credit for tax paid to NC on the MO income claimed there. See page 5 of MO-1040 Instructions
Determine SC, then NC and finally MO in that order. Pay attention to the NC tax with only the SC income vs with the MO income. The difference is what you will put on the MO tax credit form.
You could owe taxes to any of the 3 states, particularly NC. State credits are given based on the lower of tax between the states. It doesn't sound like any NC tax was paid so I would expect a bill there.
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