Asth, the different between strategy and tactic is that, with strategy, you plan out a string of actions, working towards a specific goal, while a tactic might be simply altering the way you carry out one of those actions to gain a situational advantage. What little flexibility something such as extra wood from Poseidon gives is not significant enough to have a meaningful impact on the overall strategies of people. They will still play the way they would have otherwise. If you need more wood, you can trade through the merchant, you can trade between cities and you can trade with farming villages. You can make sure you only expand farming villages using other resources and you can adjust your other unit choices to optimize resources use (using hoplites instead of chariots, for instance). There are various options, and the gods, so far, only play a limited role here. They are normally only important when it comes to battle tactics (using spells to disguise attacks, uncover others, kill catapults you couldn't defend against, diminishing enemy numbers at the right time, breaking down city walls in a coordinated action). The only place where they go beyond that and become important tactically is when they are able to reduce building time to half of what it would otherwise have been at. So, if you reduce Poseidon or Hera, the most significant change would be that it would take people twice as long to rebuild and less stuff would happen.
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