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I have a book about punctuation marks, but it doesn't report when to use | in a English sentence.
I notice that the New Oxford American Dictionary uses that character to separate the examples it reports. Are there other uses of | in a sentence written outside specific contexts?
You never use it in an English sentence. It is — as you've noticed in your dictionary — used in concise-format publications to take the place of words or more-space-taking formatting. It's also used in mathematics and pseudocode. But never in an English sentence.
I have noticed in some technical manuals, the pipe being used as a delimiter on menu interactions. For example: Edit|Copy. I used to use this as well but have since moved to using Edit>Copy instead as it feels more like a flow of commands, especially when the interactions are long and mix menus and tabs (for example: System>Preferences>Network>IP).
The vertical bar | is a piece of typography which only has meaning in specific contexts.
Personally, if I used it alone (rather than in pairs), I would probably wither be using it in the mathematical sense of divides as in "2 | n2 + n" (i.e. two divides n-squared plus n) or in the probability sense of given as in "Pr(3 heads from 3 flips|at least 2 from 3) = 1/4" (i.e. the probability of three heads from three flips given at least two from three is a quarter). There are many more uses, including as a list separator.
The | character is not part of English punctuation. You will notice that in places where it is used, such as the dictionary, near the preface you will see a section titled "How to use this dictionary" explaining the meaning of the | as used in this dictionary.
