Luke 1:68-71: "68 'Blessed be the Lord God of Israel, for he has visited and redeemed his people 69 and has raised up a horn of salvation for us in the house of his servant David, 70 as he spoke by the mouth of his holy prophets from of old, 71 that we should be saved from our enemies and from the hand of all who hate us.'"
Isaiah 61:1: "The Spirit of the Lord GOD is upon me, because the LORD has anointed me to bring good news to the poor; he has sent me to bind up the brokenhearted, to proclaim liberty to the captives, and the opening of the prison to those who are bound."
Psalm 107:10-22: "10 Some sat in darkness and in the shadow of death, prisoners in affliction and in irons, 11 for they had rebelled against the words of God, and spurned the counsel of the Most High. 12 So he bowed their hearts down with hard labor; they fell down, with none to help. 13 Then they cried to the LORD in their trouble, and he delivered them from their distress. 14 He brought them out of darkness and the shadow of death, and burst their bonds apart. 15 Let them thank the LORD for his steadfast love, for his wondrous works to the children of man! 16 For he shatters the doors of bronze and cuts in two the bars of iron.
"17 Some were fools through their sinful ways, and because of their iniquities suffered affliction; 18 they loathed any kind of food, and they drew near to the gates of death. 19 Then they cried to the LORD in their trouble, and he delivered them from their distress. 20 He sent out his word and healed them, and delivered them from their destruction. 21 Let them thank the LORD for his steadfast love, for his wondrous works to the children of man! 22 And let them offer sacrifices of thanksgiving, and tell of his deeds in songs of joy!"
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The only specific Biblical references I can find in the hymn text are the end of the third verse ("Breaking all the pow'rs of hell") and the entirety of the fourth verse:
From the bondage that oppressed us,
From sin's fetters that possessed us,
From the grief that sore distressed us,
We, the captives, now are free.
These could reference either the verse from Isaiah or the text from Psalm 107 (or both). The cited Biblical verses mention Christ's freeing us from the captivity of sin, and the hymn uses the same imagery.
The texts from Luke and the Psalms have the same general idea: praise God because He has freed us from sin, which is the same idea that the hymn expands upon: "Loudly sing His love amazing" for He has "saved us from the wily foe."
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Reading over the hymn verses, I also found some interesting features with regard to the rhyme scheme. It's AAAB, and in two verses, there's a significant shift in the text between the three A rhymes and the one B rhyme. In the second verse, the first three lines describe Christ, and the fourth (unrhyming) line mentions "the wily foe":
Christ, from heav'n to us descending
And in love our race befriending;
In our need His help extending,
Saved us from the wily foe.
Similarly, in the fourth verse, the first three lines describe the bondage of sin (a description that's enhanced by the lines' having parallel structure). The fourth line, which proclaims our freedom from sin, breaks the recurring A rhymes:
From the bondage that oppressed us,
From sin's fetters that possessed us,
From the grief that sore distressed us,
We, the captives, now are free.
The rhymes in this verse are mosaic rhymes (rhymes comprised of more than one word), which further illustrates our erstwhile captivity to sin. These mosaic rhymes work because two words (one of which is "us") are joined together. The last verse "burst[s the] bonds apart," to borrow a phrase from Psalm 107.
This is an English translation of a German text, and I'm not sure if this feature of further portraying the message of the text by means of poetic devices is in the original, but it's a great feature all the same.
