Is there a strategy to deal with questions: Which of the following must be true? Do you have to rule out every answer choice?

Here's an example: Quant Supp. Problem Solving 106.
If x and y are different integers and x^2=xy, which of the following must be true?
I. x=0
II. y=0
III. x=-y

x=y OR x=0 are the only possibile solutions. NO MORE NO LESS!!!

Yes, when they use the word "must" it means that it must always, 100% of the time be true.

When they use the word "must" your strategy is to try to prove a statement wrong - just find one instance in which it is wrong, and you know you can cross it off. If you try several different things but it keeps working, then you assume / guess it "must" be true (though, ideally, you figure out the principle behind it to understand whether it really must be true). But if it's the test and you have limited time, try different kinds of numbers (positive, negative, zero, fractions, whatever is allowed by the problem) and just go with it if you've tried 3-4 different things and it keeps working.

Another bit of strategy: assess your A through E answer choices after dealing with each roman numeral (I, II, and III). Sometimes you'll find that you don't need to try one of the roman numerals because you've already eliminated all of the answer choices that included that roman numeral. It doesn't happen a ton, but it happens enough that you should eliminate answers after dealing with each statement.

Also, do the statements in the order that is easiest for you - this kind of problem is annoying because it's long, but it does have process of elimination built right into it.