Recently I had to uninstall and reinstall my Steam library. When I reinstalled Skyrim, my game went back to vanilla. I checked Nexus Mod Manager and all of my mods have the green checkmark which suggest that they are activated.

How can I get all of my mods working again?

Check them again in the Launcher.

Do you mean the Skyrim launcher or the NMM launcher?

When I open Skyrim and go to Data Files, not all of the mods I installed have shown up.

Do you mean go into NMM and deactivate and reactivate each individual mod?

The Skyrim Launcher.

Not all show up because you likely have replacers. In which case, those may need to be reinstalled.