Learn English – Plural form of tardy

There is no rule determining whether or not a noun's plural form is the same as its singular form. As the comments point out, many of these words are words for animals. Another trend I have noticed is that loanwords from Japanese often don't change in the plural (two kanji, three Pokemon, ten anime), though sometimes they do (six ninjas, eighty futons).

From The Corpus of Contemporary American English (COCA) and The British National Corpus (BNC):

                    COCA             BNC
   octopuses      147 results       29 results
   octopi          44 results       11 results
   octopoda         4 results        0 results
   octopodes        2 results        3 results

The most common plural is octopuses. Use that.

The alternative octopi is also somewhat common. In fact, it's common enough that we should probably consider it standard as well, but because octopus isn't actually derived from Latin, pluralizing it this way may rankle some feathers. If you'd like to avoid criticism, avoid using this form.

We'll discount octopoda entirely since all four results are from Orson Scott Card's Lost Boys, in which fictional characters discuss the proper plural of octopus.

The least common on the list is octopodes. Although you can make an argument that this plural is more correct than octopi, the fact is few people know it and fewer people use it. If you pluralize octopus this way, you'll draw more attention to how you're saying it than what you're saying. Octopodes probably isn't common enough to be considered standard, and worse, it may fail to communicate entirely.

The verdict? If you want to communicate, use octopuses. Save the other plurals for when you want to use words like toys.