I am wiring three overhead florescent lights in my unfinished basement and I need 14/3 because of where the switch is located. The wiring already present between the fixtures is 14/2. I have a length of leftover 14/2 romex. Can I remove the sheathing and use each individual wire?
Short answer: NO
You may be able to use individual wires taken from a non-metallic cable (Romex is a brand) within a fixture, but not between fixtures or switches.
NEC 300.3(B) requires that:
All conductors of the same circuit ... shall be contained within the same raceway, auxiliary gutter, cable tray, cablebus assembly, trench, cable, or cord [with certain exceptions that do not apply here].
If you give us a diagram of your fixtures and switches, we may be able to suggest a solution.