How to correctly write this conditional phrase?
If you begin with a sentence in the present and you turn it into an unreal situation with an if clause ("if x were true now, y would be true now too: but x isn't true now, and neither is y"), you normally use the past subjunctive + would:
I am rich and I am arrogant
=> If I were rich, I'd be arrogant (but I'm not rich, and I'm not arrogant).
If you begin with a situation in the past and you turn it into an unreal situation in the past ("if x had been true then, y would have been true then too: but we know x wasn't true then, and y wasn't either"), you use the past perfect subjunctive and would + have + past participle:
Russian communism worked and there were no economic problems
=> If Russian communism had worked, there wouldn't have been economic problems (but it didn't work, and there were problems).
Of course other combinations are possible, but this is the basic system. If you have a two- or threefold condition, as in your example, the tenses used depend on two things:
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Is the main situation supposed to be an unreal situation in the past or in the present?
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Are the parts of the condition (the if clauses) supposed to be happening at the same time, or did one happen before the others? If they didn't happen at the same time, those that were earlier than the "main" situation should be put in a tense that precedes the tense of the main situation (if possible): if the main situation is an unreal situation in the present, earlier parts should be in the past perfect subjunctive.
Let's assume that your example is about an unreal situation in the present ("if x were true now, y would be true now too"). It matters then whether all three things happened at roughly the same time—in this case, in the order by which they are mentioned: first A, then B, then C—or the assignment was given before the vacation.
If you were given this assignment before your vacation, this should be marked by putting the "assignment" if clause in the past perfect subjunctive ("had given"), to show that it happened before the "vacation" if clause. If your professor called you during your vacation to give you this assignment, you would simply use the past subjunctive ("gave").
Do you perhaps like the sound of
If I were a student, and it were my vacation, and my professor had given me this assignment, I would do xyz ...
any better?
What about:
If I were a student and my professor gave me this assignment on my vacation, I would do xyz...
While it eliminates one of the ands I find it easier to read.
I don't think your version is bad, really. I'd probably do something like
If I were a student and it was my vacation, and if it was my professor that had given me the assignment, I'd xyz the xyz.
This isn't based on explicit rules, but on a sense of how it I could emphasize the nested conditionals as belonging within another (counterfactual?) condition.
Here's an option that takes more liberties with your original clauses.
"If I were a student, and my professor assigned something over break, I'd [put it off 'til the last minute and complain about it]." (That's actually a true story ;_;...)
You lose a little informality with the single "and," but I think the other changes I made make up for it.
Good luck!