To forestall a pedantic nitpick, there are some that claim that “poisonous” applies only to plants or animals that have toxic compounds in their tissues, while “venomous” should be restricted to animals that inject toxic compounds. I’ve never found a basis for the former technical distinction. “Poisonous” can be applied to both organisms that are themselves toxic, and those that inject venom. “Poisonous snake” is a perfectly valid description.
In present usage, however, “venomous” is usually restricted to organisms that inject toxins. One would not speak of a “venomous plant,” for example. However, there is precedent for a broader use; Shakespeare spoke of the “venomous toad.” But that use today is somewhat archaic.
According to this, birds like the pitohoui would typically be called poisonous rather than venomous.