Services

Services are injectable classes that usually are instanciated by the DI system.

Utility functions

I don't see a problem with injecting utility classes into services or components (while just importing them without the DI would make testing much harder).

utility classes shall be instanciated in app.module.ts rendering them into application global singletons.
they may import their methods from external files (test those files individually!).
methods probably shouldn't know about each other, they are static in nature.