This means that should an Ö occur in English text, it is to be treated just like a regular O unless there is also a version without the diacritic, as might occur with coöperate and cooperate or co-operate. Those three all have the same letters in them as far as English is concerned, differing only in non-letters.
Note that only letters are supposed to be considered when sorting text. One ignores non-letters such as spaces, hyphens, dashes, or full stops, when sorting English text. That means that thesethe five imagined book-titles below are correctly sorted as text in this fashion:
Diacritics are rare in English words, occurring only in loanwords or words marked for poetic meter, as in learnèd or Faërie. As such Being so rare in the first place, the ordering of different diacritics against each other (like é vs. è vs. ê vs. ë) may not be especially well defined in older dictionaries. The caseneed for distinguishing those is rare enough that I haven’t yet found ana single example of itthis in the OED. The classic French example of cote < côte < coté < côté does not apply to English because we do not have all those words as separate in any English dictionary.
Modern English has no such special needs apart from the unusual case of sorting people’s names, although words spelled with the lexical ligatures æ and œ must be treated as though those wellif spelled with two characters instead of one, so as though those were ae and oe respectively. That means that Cæsar sorts as though it were Caesar and œuvre as though it were oeuvre.