Can articles be omitted in front of the second and third nouns?

Leaving out the articles is grammatical. But we're more likely to leave out repeated definite articles than indefinite ones. See Ngram. And we're much more likely to leave out the article when the items are connected. For example, Ngram shows "a car and trailer" is more common than "a car and a trailer"; but "a car and house" is less common than "a car and a house" (although both forms are used in both cases).

And while "he gave me a box of chocolates and bouquet of roses" sounds fine to me, I think you really should put two articles in "he gave me an octopus and bouquet of roses".