Ah, the Big Kahuna of symbolism in "Journey of the Magi," and it's all crammed into the middle stanza. The second bit of this poem can be interpreted as an allegory for a couple of different things in the Bible. And because it's so jam-packed, we're going to go through it with a fine-toothed comb here, Shmoopoets.
Line 23: If we look at water in the Bible, one of the more prominent bodies is the river Jordan, which is where John the Baptist does his thing. (You can find references to it in both the Old and New Testaments, in nearly every Gospel.) The running stream, then, could allude to the significance of the Biblical river. But the water mill is less obvious. The "mill" part of it would seem to refer to a grain mill of some kind, and water-powered. Critics have pointed to Matthew 3:12 here, in which Christ's "winnowing fan of judgment" separates the wheat (the good) from the chaff (the sinners).
Line 24: We talk about the three trees a little bit in the "Summary" section, but we'll go over it again: the trees here seem to correspond directly with the three crosses on Golgotha, which is the hill upon which Jesus and the two thieves were later crucified.
Line 25: As it turns out, when we look up white horses in the Bible, we get two really scary bits, namely Revelation 6 and 19:11-16. The first one describes the four horses of the Apocalypse, which bring takeover, war, scarcity, and widespread death to the people on earth. The first horse, the horse of conquest, is white. The second passage is even more telling, and is called "Christ on a White Horse" and depicts Jesus coming back down to earth to do battle with Satan and his minions (i.e., corrupt kings of men).
Line 26: The tavern's lintel might be symbolic of the tenth plague in Exodus, which was the killing of all firstborn children. To get out of having this plague inflicted upon you, you had to mark your doorpost, or lintel, with the blood of a lamb. The vine-leaves could also refer to John 15:1-5, in which Jesus is depicted as a vine, with his followers as leaves and branches.
Line 27: The "dicing for pieces of silver" bit of this line alludes to two separate events in the Bible. First, to the betrayal of Jesus (Judas did it for 30 pieces of silver), and then to the Gospels, in which four Roman soldiers cast dice to see who gets what bits of Christ's clothing after he's been killed. (Note: that's also a double allusion, to Psalm 22:18.)
Line 28: The wine-skins here could be symbolic of a bunch of stuff. One of Jesus' first miracles was the water-into-wine trick (John 2), and the mini-parable in Matthew 9:16 seems to imply that Jesus will be the "new wine" (i.e., the new religion) to be put into "new wine-skins." So the kicking of the empty old wine-skins in the passage signals the big religious change that's coming.
Line 31: The single word "satisfactory" here has caused critics no end of consternation, but the current consensus seems to be that the word is a reference not to the Bible but to Article 31 of the Anglican Articles in which Christ's sacrifice is the ultimate satisfaction of the debt of all man's sins. Remember that this poem was written directly after Eliot's conversion to Anglicanism.