余 / 吾 + [verb phrase]
吾 + [noun]
吾辈 / 吾等 + [verb phrase]
余 and 吾 both mean "I" in classical Chinese. Neither is used in speech. You meet them in quotations, in prefaces and old letters, and in modern essays where the writer wants an old-fashioned or mock-solemn voice.
吾 can stand straight before a noun and mean "my" or "our", with no 的.
吾辈 – "people like us", "our generation" – is still alive in written rallying calls and in prefaces. 吾等 is "we" in the voice of a historical novel.
余 more often means "remaining" or "more than": 其余 "the rest", 三十余人 "more than thirty people". The "I" reading has a verb right after it, usually at the start of a clause.
A modern writer who uses 吾 is being playful or grand on purpose. Swapped into an ordinary sentence, it sounds like a joke.
汝 is the matching classical "you", and turns up in the same kinds of text.