There are many ways to read a myth. The Greek philosopher Xenophanes would have seen Zeus' amours as allegories, while Euhemerus would have looked for the history behind the myth. (And, as my link points out, those who see them as the "marriage" of invading sky-gods to local earth-goddesses continue that tradition.)
In modern times, Robert Segal wrote a brief but interesting book interepreting the Narcissus myth in many different ways (archetypal [Jung], structuralist [Levi-Strauss], ritualist [Frazer], etc.). You could certainly do the same with any of these Zeus myths.
As for why those specific animals, the eagle was Zeus' (and Jupiter's) special animal, and the bull was important to the Cretans, as well as the animal of both Zeus and Poseidon. The swan was associated with Aphrodite, the goddess of love, which may have suggested the shape to Zeus. I'm not sure about the shower of gold, which sounds painful. (Perhaps Zeus had a fit of realism, and figured that even if Danae didn't want him, she could use the gold.)