Well, if they spoke as they did 3000 years ago, it would be all Greek to us.

But, putting the need for translation aside, who says their ways of speaking have changed? Maybe they've been punning for a long time. Or maybe, being immortals, the older ones got bored of straightforward speech a few centuries ago and started playing with words more, just like the gods. Or maybe they don't pun very much, but Diana has picked up a bit of the habit from Ares and other gods with whom she has interacted.
Why Zola is able to understand the language on Paradise Island is another matter, but probably the kind of thing it's best not to worry too much about. I really don't want comics to have to get bogged down making up explanations for stuff like that.
ETA--
Here's something Azzarello said about the gods' use of language shortly before his run started:
But it has been pretty enjoyable coming up with the dialogue and the cadence of these characters that are larger than life, the way that they speak. They have a sort of larger than life approach to sentence structure too! [Laughs]
I think part of his thinking may be that the gods just wouldn't use language in a straightforward, ordinary way, but would play with it and twist it around, if only to keep themselves amused.
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