I was listening to the We Three Kings Christmas carol, and I ended up taking note of the syntax. Given the use of the thou/thy/thee/thine pronouns for the second-person singular and the vocative particle O, it seems to be using a rather archaic form of English. Having said that, I'm unfamiliar with some of the syntax, and I wondered if, as a song, it is quite similar to Shakespeare's works in that it was, even at the time of writing, ungrammatical to arrange the words as they were, but done anyways for aesthetic purposes (in the song's case, to rhyme and work with the music).

For punctuation and capitalization, I've referenced the Hopkins, Carols, Hymns, and Songs, 1st ed., 1863 lyrics on the Wikipedia page.

We Three Kings of Orient are,
Bearing gifts we traverse afar,
Field and fountain,
Moor and mountain,
Following yonder Star.

"We Three Kings of Orient are" has an SOV arrangement. "Bearing gifts we traverse afar" seems like it has a punctuation issue—assuming the "bearing gifts" part is a subordinate clause, there should be a comma between it and "we traverse afar". "Following yonder Star" has no subject.

O Star of Wonder, Star of Night,
Star with Royal Beauty bright,
Westward Leading,
Still Proceeding,
Guide us to Thy perfect Light.

I'm guessing that because of the capitalization, "Royal" is not really considered an adjective in this and is part of a compound noun in "Royal Beauty". What confuses me about this is the fact that the adjective "bright" comes after the noun.

Born a King on Bethlehem plain,
Gold I bring to crown Him again,
King forever,
Ceasing never,
Over us all to reign.

"Gold I bring to crown Him again" has an OSV arrangement. "Over us all to reign" is an OV arrangement without a subject.

Frankincense to offer have I,
Incense owns a Deity nigh:
Prayer and praising
All men raising,
Worship Him, God on High.

"Frankincense to offer have I" is an OVS arrangement.

Myrrh is mine; its bitter perfume
Breathes a life of gathering gloom;—
Sorrowing, sighing,
Bleeding, dying,
Sealed in the stone-cold tomb.

I'm confused about the punctuation of the second line—most of the other lines end in commas or periods (I see it a lot song lyrics and poems), but this one ends in a semicolon followed by an em-dash. "Sealed in the stone-cold tomb" does not have a subject.

Glorious now behold Him arise,
King, and God, and Sacrifice;
Heav’n sings Hallelujah:
Hallelujah the earth replies.

"Glorious now behold Him arise" is difficult for me to analyze—I can't figure what is the subject, what is the object, why "glorious now" is at the beginning, etc.

If I had to guess, I would say that many of "ungrammatical" things I pointed out are were actually grammatical at one time, but there probably are some elements that do forgo proper syntax in favour of artistic expression as well. Still, I would like to know what things were accurate parts of archaic grammar and how they work.

I was listening to the “We Three Kings” Christmas carol, and I ended up taking note of the syntax. Given the use of the thou/thy/thee/thine pronouns for the second-person singular and the vocative particle O, it seems to be using a rather archaic form of English. 

Having said that, I’m unfamiliar with some of the syntax, and I wondered if, as a song, it is quite similar to Shakespeare’s works in that it was, even at the time of writing, ungrammatical to arrange the words as they were, but done anyways for aesthetic purposes (in the song’s case, to rhyme and work with the music).

For punctuation and capitalization, I’ve referenced the John Henry Hopkins collection Carols, Hymns, and Songs, using the 1st edition’s 1863 lyrics from the Wikipedia page. and the enlarged 2nd edition’s 1872 lyrics from Google Books.

We Three Kings of Orient are,
Bearing gifts we traverse afar,
⁦        Field and fountain,
⁦        Moor and mountain,
Following yonder Star.

We Three Kings of Orient are has an SOV arrangement. Bearing gifts we traverse afar seems like it has a punctuation issue — assuming the bearing gifts part is a subordinate clause, there should be a comma between it and we traverse afar. Following yonder Star has no subject.

O Star of Wonder, Star of Night,
Star with Royal Beauty bright,
⁦        Westward Leading,
⁦        Still Proceeding,
Guide us to Thy perfect Light.

I’m guessing that because of the capitalization, Royal is not really considered an adjective in this and is part of a compound noun in Royal Beauty. What confuses me about this is the fact that the adjective bright comes after the noun.

Born a Kɪɴɢ on Bethlehem plain,
Gᴏʟᴅ I bring to crown Him again,
⁦        King for ever,
⁦        Ceasing never,
Over us all to reign.
⁦                O Star, &c.

Gold I bring to crown Him again has an OSV arrangement. Over us all to reign is an OV arrangement without a subject.

Fʀᴀɴᴋɪɴᴄᴇɴꜱᴇ to offer have I
Incense owns a Deity nigh :
⁦        Prayer and praising
⁦        All men raising,
Worship Him Gᴏᴅ on High.
⁦                O Star, &c.

Frankincense to offer have I is an OVS arrangement.

Mʏʀʀʜ is mine ; its bitter perfume
Breathes a life of gathering gloom ; ⸺
⁦        Sorrowing, sighing,
⁦        Bleeding, dying,
Sealed in the stone-cold tomb.
⁦                O Star, &c.

I’m confused about the punctuation of the second line — most of the other lines end in commas or periods (I see it a lot in song lyrics and poems), but this one ends in a semicolon followed by an em dash. Sealed in the stone-cold tomb does not have a subject.

Glorious now behold Him arise,
Kɪɴɢ, and Gᴏᴅ, and Sᴀᴄʀɪꜰɪᴄᴇ  ;
Heav’n sings Allelujah :
Allelujah the earth replies.
⁦                O Star, &c.

Glorious now behold Him arise is difficult for me to analyze — I can’t figure what is the subject, what is the object, why glorious now is at the beginning, etc.

If I had to guess, I would say that many of “ungrammatical” things I pointed out are were actually grammatical at one time, but there probably are some elements that do forgo proper syntax in favour of artistic expression as well. Still, I would like to know what things were accurate parts of archaic grammar and how they work.