work at something

努(つとめる)	Make an effort (at improving your French, at quitting smoking, to be nice to your friend’s douche boyfriend, etc.), more like 頑張る than the other つとめるs. $$$

務(つとめる)	Perform a specific task or role which you have been assigned (but not necc. at a job)

勤(つとめる)	Work (used only about a job, and not in reference to a particular project at that job) (emphasis is on the physical work rather than the role).