When to discard with Oasis
You do everything on the card in the order it says:


Draw one card.
Add one to the number of remaining actions you have for the turn.
Add one coin to the amount you have to spend this turn.
Discard a card.


And then you can move on to other Actions or your Buy phase. So you'll discard a card before you play any other actions. (But it's during your Action phase, of course - it has to be since you played Oasis!)