wrapped in pieces of cloth

The custom of that time was to tightly wrap newborn babies in long strips of cloth. It may be necessary to say, "wrapped in long strips of cloth, in the customary way."

feeding trough

That is, "animal feeding box." Also see how you translated this in 23:05.

filled with angels

This means that there were so many angels that they seemed to fill the sky.

Glory to God

This can also be translated as, "Let us all give glory to God!" or, "Our God deserves all glory and honor!" or, "We all give glory to God!"

peace on earth

Another way to say this would be, "may there be peace on earth."

the people he favors

This might be translated as, "people that God looks upon with favor, delight, or good will."

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