at work, how do you ask someone nicely to do a task themselves (when they're trying to offload it on to you when they could and should do it themselves)?

Depends on job, culture, and work title.

Some jobs are a "yes sir, right away, sir" situations. Some jobs are, "that isn't my department, contact ____ for assistance with ". Other times it is your job, but not your primary focus, so you can say, "I am unable to help at this time due to an increase in demand for ___,".

Don't be overly accommodating unless that's your job duty.

My primary responsibilities are my main job. I only help with extra things if I want or am instructed by my upper level managers. And then, it's usually somewhere in my secondary duties list or it's not something they would feel comfortable asking me to do. But I've seen work cultures where you are expected to go above and beyond your resume roles, unpaid, to do extra work, and that's just how working there is.

Figuring out your work culture guidelines is #1 to answering this question.

/r/AskWomen Thread