It is my understanding that 'octopuses' is the strictly correct option because it matches a greek root word with an English suffix and we are speaking English after all. Dictionaries seem to agree.
Octopodes is acceptable in some contexts because it matches a greek root word with a greek suffix. Octopi is just wrong because it applies a latin suffix to a greek root.
This came up notably a few years ago as the winning answer to a high-stakes HQ Trivia game. [1]
If we were speaking Latin, would “Octopi” still be wrong? Given the logic used to claim that Octopuses is the correct pluralization, I don’t see how it could be.
Thus, I’m left to conclude that Octopodes is the only correct form since it lacks this spoken language dependency.
See my sibling comment - where does the insistence that octopus is third declension come from? The reality is that while most Greek loanwords are third declension, many are not, and Latin authors tended to not be consistent.
Octopodes is acceptable in some contexts because it matches a greek root word with a greek suffix. Octopi is just wrong because it applies a latin suffix to a greek root.
This came up notably a few years ago as the winning answer to a high-stakes HQ Trivia game. [1]
[1] https://www.nytimes.com/2018/01/05/arts/hq-trivia-app-appoin...