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Let's take Thassa, God of the Sea as my god. When does it count as a creature?
If I cast Thassa and my oponent has Kambal, Consul of Allocation, does it trigger Kambal ability?
Can Essence Scatter counter Thassa?
If I cast Thassa and my oponent has Authority of the Consuls, does it trigger?
Can I put Thassa into play discarding it with Æther Rift
The devotion ability on the Theros gods are Static Abilities, covered by rule 604.2.
[emphasis mine]
604.2. Static abilities create continuous effects, some of which are prevention effects or replacement effects. These effects are active as long as the permanent with the ability remains on the battlefield and has the ability, or as long as the object with the ability remains in the appropriate zone, as described in rule 112.6.
Static abilities, like the one on the Theros gods, only function while on the battlefield unless otherwise stated as part of the ability, they define costs or special ways to counter the spell on the stack, they are characteristic defining, or the object type only exists in zones other than the battlefield (command zone usually, like emblems).
Of these special conditions, the only one close for the theros gods creature type is Characteristic Defining. The test for characteristic defining is laid out in rule 604.3a. The Theros gods fail that due to condition 5 of that rule, as devotion is a condition.
604.3a A static ability is a characteristic-defining ability if it meets the following criteria: [...] (5) it does not set the values of such characteristics only if certain conditions are met.
As for your specific questions:
These are all covered by the Gatherer rulings (also repeated on magiccards.info where you linked to).
Thassa is always a creature when not on the battlefield, so casting her doesn't trigger Kambal, Essence Scatter can counter her, and Aether Rift can put her into play:
9/15/2013: The type-changing ability that can make the God not be a creature functions only on the battlefield. It's always a creature card in other zones, regardless of your devotion to its color.
She's only a creature when she enters the battlefield if you have the devotion, so she may or may not trigger Authority of the Consuls (and it may or may not cause her to enter tapped):
9/15/2013: If a God enters the battlefield, your devotion to its color (including the mana symbols in the mana cost of the God itself) will determine if a creature entered the battlefield or not, for abilities that trigger whenever a creature enters the battlefield.
This is because the devotion-checking ability is a static ability, so it only functions while Thassa is on the battlefield. When she's not, the ability does nothing, so she's just a creature as printed.
112.3d Static abilities are written as statements. They’re simply true. Static abilities create continuous effects which are active while the permanent with the ability is on the battlefield and has the ability, or while the object with the ability is in the appropriate zone. See rule 604, “Handling Static Abilities.”
(There are more details, but that's all that really matters here. Notably it's not a characteristic-defining ability, which would function in all zones, because it's conditional.)
