I think you must be
Verse
Very important, are the lines that I write,
A verse is a group of lines that form a unit in a poem or song
Certain words, they won't appear quite right.
Usually to fit a rhyme or structure, words need to be moved around.
Harmony accompanies me, to those who listen,
Verse writing is usually arranged in a metrical rhythm and usually ha a rhyme scheme which is favourable for musical arrangement.
Poised elegantly, by those who have written.
Verses are intentionally written with such structure.
Bibles and songs hold me within their pages,
Each of the short numbered divisions of a chapter in the Bible is a Bible verse, songs are often divided into verses
I've appeared everywhere, throughout the ages.
Writing in verse is quite common.
Additional hint
Taking the first letter of the first line, the second of the second line,... and the fifth of the fifth line spells out VERSE