The oracle is primarily used to answer yes-or-no questions about the world. So, when you have a question and your character isn’t directly involved—for example, “Is the weather good?” or “Is that NPC friendly toward me?”—this is when you would use the oracle.
As for the evade action, you use it when the fiction indicates that you should. For example, if you do something and ask a question using the oracle—“Does that NPC attack me?”—and the answer is yes, you would probably use the evade danger action to resolve the situation. The other way to use it is when another action specifically tells you to do so.