Dark-Dweller Oracle doesn't change when you can cast the exiled card. For example, if you exile a sorcery card, you can cast it only during your main phase when the stack is empty. If you exile a land card, you can play it only during your main phase and only if you have an available land play remaining.

Casting an exiled card causes it to leave exile. You can't cast it multiple times.

If you don't cast the exiled card, it remains in exile.

You can sacrifice Dark-Dweller Oracle to pay the cost for its own ability.