Does "Oh" count as an interjection in "Oh, no," that is, should there be a comma after the "Oh?" For example:

"Oh, no," she said under her breath.

Or is it just a stylistic thing, rather than a grammatical one?
Yes, it's an interjection. Use a comma.

Generally speaking, there's no need to place a comma before no in Oh no(!). Usually, it is perceived as one
grammatical unit. Consider this example: "Oh no! I've left my keys in the room".


Oh, that's fantastic!
Oh, I'm very sorry to hear you were treated unfairly.

However, if no is used as an answer to a question and oh is for emphasis, then placing a comma before no is

-- Have you ever been to the UK?
-- Oh, no.

Students: We have free audio pronunciation exercises.
See Chicago Manual of Style, 16 edition, section 5.208. No comma needed.
Teachers: We supply a list of EFL job vacancies

According to the Chicago Manual of Style, section 6.35, 17th edition, no comma is needed with "Oh no."