Spell is cast which says choose one of each ' Creature, Artifact, Enchantment' sacrifice the rest. If you have a creature which is also an artifact, or creature who turns into an enchantment as a result of the sacrifice. If you choose a permanent with more than one type does it count as more than one type in this case.
A permanent counts as each of the types it is. So an Artifact Creature (like Darksteel Colossus would be both an artifact and a creature.
For a spell like Cataclysm, you could choose an artifact creature as the choice for the artifact, or for the creature, or choose it for both if you want (which would cause you to sacrifice more permanents than you have to). If you had 2 artifact creatures, you could choose one of them as your artifact to keep, and one as your creature to keep; thus keeping them both.
See the Gatherer Rulings on Cataclysm
If you control a permanent with more than one type, you can choose that same permanent for more than one of the choices if you want to. This makes it possible to select an artifact creature as both your artifact and creature, and then select a land and thereby keep only two cards.
If you control a permanent with more than one type, you can choose that permanent to be the representative of either type. This makes it possible to have more than one creature (or other permanent type) on the battlefield. For example, if you select a creature for your creature and an artifact creature for your artifact, you get to keep both of these creatures.
From the comprehensive rules:
205.2b Some objects have more than one card type (for example, an artifact creature). Such objects satisfy the criteria for any effect that applies to any of their card types.
Specifically the enchantment creature that changes as a result of the sacrifice (presumably a God from the Theros block), it's still a creature before the sacrifice, and only becomes not a creature when the ability resolves. So you can choose it as the creature, an artifact creature as the artifact, and another enchantment creature as the enchantment. Or choose the God as the enchantment because it's always the enchantment. Or any number of different scenarios.
Long story short, if you have permanents that are multiple types, you get to choose how they are defined so that you get the most benefit.