The Inspired abilities might trigger during your untap step, but triggers can't go on the stack in that step. In essence, they will work like an upkeep trigger and you can order them along with any other upkeep triggers you need to put on the stack at the same time!
Gods that enter while you have 4 devotion will be a creature when they enter, even though they aren't entering "as a creature." This is confusing, but we explain how that difference matters for enter-the-battlefield triggered abilities!
We delve into a tricky rules interaction with gods entering the battlefield while devotion to their color is exactly 4 before they enter.