How many syllables does e'er have?

Answer 1

Most dictionaries say one. But rhyming dictionaries give some two syllable rhymes.

Most people I have heard pronounce it in speech, which isn't very many, give it a kind of glitch but not a full stop at the apostrophe. In song it can have several syllabels if drawn out. E'er is mostly used in poetry where a one syllable rhyme or beat is needed.

The "glitch" pronunciation, sorta "eh er," may be just because ever is two, or because of the apostrophe, or to differentiate it from ere as in "Able was I ere I saw Elba." or err as in "To err is human..."

Two syllables could be mistaken for error. Which could be an error, the correct form would be one syllable, Err. Same for o'er, oar not oh-ur.
E'er is a poetic word used to make the meter of the poem sound correct. It has only one syllable.