Learn English – “Not a thing” versus “nothing”

In those short sentences you give as examples, they can be interchangeable for normal, everyday use. That they are interchangeable here could be due to insufficient context around the sentences. Can versus could is more subtle than may versus might, or can versus may. Could is more subjunctive, tentative, but can is more firm - at least in this context.

What I want to express is that yesterday was my last day of work for this year and I have two weeks off work from today...

I think all three of your sentences pretty much say the same thing, but none of them quite say what you are trying to express.

Let's start with the sentence "I'm done with all my work this year." To me, that sounds as though you had a certain amount of work assigned to you for the year – maybe it was to build 400 widgets on an assembly line, or teach 15 training courses for a company, or keep three accounts balanced – and now all that work is done.

Having all your work done for the year is not quite the same thing as being done with work for the year.

I'm done with all my work for the year.

means there is no more work to be done. You inbox is empty, all your annual goals are met. If you walked into the office on Monday, you would have nothing to do but twiddle your thumbs and stare at the walls. On the other hand:

I'm done working for the rest of the year.

means that you will be vacationing until January. Yes, there may still be emails to answer, reports to write, widgets to build, or sales quotas to be met, but all of that will have to wait until you get back to work.

The three sentences you gave all sound like they mean "There is no more work for me to do; I've finished everything, and I won't need to work again until January." They have a feel of, "Mission accomplished." I wouldn't expect a salesperson who works off of commissions to ever say that – even if quotas or goals have been met, there's always one more sale that could be made. However, a professor at a university might say that, once all the exams have been graded and the final grades have been turned in.

However, being done with work because you're scheduled to take two weeks off is a different matter. You realize there's always more work that could be done, you just won't be there to do it for two more weeks. If that's what your trying to communicate, I'd use one of these instead:

I'm all done working until next year.
I will be off work until next year. (or, more briefly, I'm off till next year).
I won't be coming in for the rest of the year.