Is OIL independent from the rest of Fuel or would I need to update the entire framework to update OIL? I want to do this because I want to disable pluralizing.
Oil is a package like all others. It just uses the framework, it doesn't use any dirty tricks under the surface.
Offcourse, the version of oil (all packages really) requires the same version of the framework, so if you update one, you might find you need to update the others too.
If you really need to make modifications to FuelPHP code, clone the git repository locally, create a new branch for your features, and change it in there. If a new release comes out, switch back to the FuelPHP branch, update it, and merge the changes to your feature branch.
Any conflicts between the changes introduced by the update and your code will be quickly visible.