Which of the following quotations contains an allusion?
"His foray had failed;/the harm-wrecker rued his raid on Heoret."
"Where had the horse gone? Where the man? Where the giver of gold?"
"[A]s a fay-man fell he passed,/ and green all over glowed."
"Redeth Ecclesiaste of Flaterye. / Beeth war, ye lords, of his threcheye."
I believe it's the last one, but I'm not certain.
Only one of the four quotations, I suspect, is from Beowulf: the first (because of the reference to Heoret). The second is from The Wanderer. The third is from Sir Gawain and the Green Knight. The fourth is from the Cantebury Tales.
At first, I didn't think any of them contained an obvious allusion, because I was thinking of an allusion as "an indirect reference." A common (and probably more accurate) definition of allusion is "a quick or passing reference." Using this second definition, the two previous posters are absolutely right: the fourth quotation, with the passing reference to a book of the Bible, is the one with the allusion.
I agree that you are right. Allusions are quite often identifiable too by capital letters because you then know that they are proper nouns. In this both the first and fourth lines give you that indicator. However, proper nouns are not always allusions, thus in the first set of lines' case.
Sometimes too, an allusion will refer to something famous without being capitalized. For example, some people call good-looking women sirens because they are attractive and sensual like the women of The Odyssey. But they doen't capitalize the letter.
In your case the 4th is correctly an allusion to the bible.
I believe that you are right about this. Remember, an allusion is when a writer speaks of something (or has a character speak of something) that is well known to most people. Typically, this will need to be a famous person or place, or some piece of literature that is famous.
In this case, the only one that makes sense is the last one. It is referring to the Book of Ecclesiastes in the Bible.
You do not specify where these quotes come from, but if they are not from Beowulf, then the first quotation could be an allusion to that epic poem.