Following are a number of back-translations of Luke 2:14:
Noongar: “‘Great, great thanks to God, high in his Holy Country, and peace on our Earth. Peace to all good people. God is happy with them.'” (Source: Warda-Kwabba Luke-Ang)
Uma: “‘Come let us worship God who is in heaven! and on earth, people whom he likes receive goodness of life.'” (Source: Uma Back Translation)
Yakan: “‘God is worthy to be praised in heaven and on earth may the people who please God be in peace/have peace.'” (Source: Yakan Back Translation)
Western Bukidnon Manobo: “they said, ‘Let us (inc.) praise God who is in Heaven. And here on the earth may the situation become peaceful of all those people with whom God is pleased.'” (Source: Western Bukidnon Manobo Back Translation)
Kankanaey: “‘God in heaven is honored/praised. The people on earth who make-him-happy will-be-at-peace.'” (Source: Kankanaey Back Translation)
Tagbanwa: “‘Praise God who is in the high-part of the sky/heaven. And here under the heavens, peace/protection of mind/inner-being is what he will give to people who are pleasing to him.'” (Source: Tagbanwa Back Translation)
Kupsabiny: “God is big/great in heaven/up | peace is coming | to people who please/love God.” (Source: Kupsabiny Back Translation)
Bariai: “Let’s lift up Deo’s name who is living very high up! | And the people on earth whom Deo is happy with, his action of peace (lit. “of a smooth interior”) remains with them.” (Source: Bariai Back Translation)
Mairasi: “‘We who are in the Heaven, we must honor Great Above One [God]! And then you guys, you who live in the world, you who are in Above-One’s vision [who are pleasing to Him], good peace is intended to be yours!’ said they.” (Source: Enggavoter 2004)
HausaCommon Language Bible: “’Glory to God over there in heaven! | On earth let peace it remain | together with those whom God he feels pleasure of them!’” (Source: Hausa Common Language Back Translation)
Pfälzisch translation by Walter Sauer (publ. 2012): “Honor belongs to God in heaven | and peace shall reign on earth | among the people | because he loves them.”
Low German translation by Johannes Jessen, publ. 1933, republ. 2006: “Praise and honor for God the Lord above | and peace down here on earth for people who mean it with all their heart and have the favor.”
Hawai’i Creole English: “Up in heaven where God lives, | may he continue to be awesome! | And here on earth | If God likes what people are doing | He’ll make their hearts rest within them.” (Source for this and two above: Zetzsche)
English: “‘God is great! He lives in the highest place above. | He will bless the people on earth who please him. | They will have peace in their minds.’” (Source: EasyEnglish Bible)
English: “‘May all the angels in the highest heaven praise God! And on the earth may the people to whom God has shown his favor have peace with him!’” (Source: Translation for Translators)
The phrase that is translated into English as “uncircumcised in heart and ears” is translated into Afar as “You are people who have hearts that refuse God, and ears closed saying we didn’t hear God’s message.” (Source: Loren Bliese)
Other translations for “uncircumcised in heart and ears” include:
Rincón Zapotec: “it doesn’t enter your hearts or your ears. You are like those who don’t even believe”
Morelos Nahuatl: “you have your heart as unbelievers, you do not want to hear God’s word”
Highland Popoluca: “you never wanted to do God’s will, never truly believed”
Teutila Cuicatec: “you are just the same as those who do not believe God’s word because you do not obey”
Huichol: “you have not been marked with God’s sign in your hearts or in your ears” (or: “you are unruly and unsubmissive like an untamed, unbranded bronco”)
Ojitlán Chinantec: “you do not have the word-sign in your hearts. Your ears are clogged”
Isthmus Mixe: “your hearts and minds are not open” (source for this and above: Viola Waterhouse in Notes on Translation August 1966, p. 86ff.)
Kaqchikel: “with your hearts unprepared” (source: Nida 1964, p. 220)
Elhomwe: “like people who do not know God” (source: project-specific translation notes in Paratext)
Chichewa (interconfessional translation) “hard-headed.” (Source: Wendland 1987, p. 130)
Bariai: “You aren’t able to receive knowledge, certainly not. You shut your ears always to Deo’s talk.” (Source: Bariai Back Translation)
Low German 1975 translation by Rudolf Muuß: “Your hearts and ears are no better than those of the heathen”
Uma: “No kidding your stubbornness! No kidding your making yourselves deaf to hearing the Word of the Lord God!” (Source: Uma Back Translation)
Yakan: “Your livers are livers not obeying/following God. And how deaf are your ears. You do not listen-to/heed God’s word/message.” (Source: Yakan Back Translation)
The Greek that is translated as something like “worried (or: anxious) and bothered about many things” is translated in Tzeltal as “doing all kinds of things has gone to your heart and you have difficulty because of it” (source: Reiling / Swellengrebel) and in Bariai as “You are concerned (lit. your interior is here and there) and worried (lit. you have various interiors) about very many things” (source: Bariai Back Translation).
In the German New Testament translation by Berger / Nord (publ. 1999) it is translated idiomatically as ich will dir anerkennen, dass du vor lauter Machen und Tun nicht weiß, wo dir der Kopf steht or “I will acknowledge that you don’t know where your head is because of all the doing and making.”
The term that is translated as “worried (or anxious)” in English is often translated idiomatically. Examples include “eating for oneself one’s heart” (Shona, version of 1966), “black with worry” (Chichewa), “breaking one’s head” (Sranan-Tongo), “hanging up the heart” (Bulu), “crumbling in one’s abdomen” (Western Kanjobal), “one’s stomach is rising up” (Farefare), or “one’s mind is killing one” (Navajo). (Source: eiling / Swellengrebel)
The Hebrew and Greek that is usually translated into English as “peace,” when referring to one’s inner peace, is (back-) translated with a variety of idioms and phrases:
“rest the heart” (Central Mazahua) / “rest within” (Lacandon) (source: Nida 1952, p. 40 and 128ff.) / “wait well in your heart” (Yatzachi Zapotec) (source: Viola Waterhouse in Notes on Translation August 1966, p. 86ff.)
The Greek terms that are translated as “reconcile” and “reconciliation” in English are translated in various ways. Nida (1952, pp. 140) says this:
“The North Alaskan Inupiatun describe reconciliation in the simple terms of ‘making friends again.’ That is to say, ‘God was in Christ making friends again with the world.’ The Uduk in the Sudan express this same truth, but in the rather interesting phrase ‘meet, snapping fingers together again.’ This expression is derived from the Uduk’s practice of snapping fingers together when they meet each other. Instead of shaking hands, they extend their thumbs and middle fingers and snap fingers together, but only friends will do this. Men who have something against each other refuse to acknowledge each other in this way. And so it is that the natural man is an enemy of God; he refuses to snap fingers with God, but God has come to reconcile man to Himself and through Jesus Christ has brought man into fellowship with Himself. Man and God may now meet ‘to snap fingers together again.’
“The Tai Dam of Indo-China employ quite a different figure of speech. They say that reconciliation consists in ‘rubbing off the corners.’ This does not refer to social acceptability, but to rubbing off the corners so that two objects, meant for each other, will fit together. Man is regarded as being incapable of fitting into the plan and fellowship of God because of the sin which has deformed him and which stands out as an ugly growth on his personality. The corners of iniquity must be rubbed off so that man may be reconciled to God and made to fit into God’s eternal plan for the world.”