In the "Underworld" there's not a whole lot of strategy to be done other than how you pick your characters, and even there we are limited to the choices given.
There is a bug that could be fixed that would allow a little more strategy. This will take some explaining:
Occasionally, the Floating God will take one of your guys and you will lose the rest of your health in a single round, resulting in 4 guys lost. After this happened a few times I realized I could pay attention to the screen as to which colors will be chosen to be "taken" after health lost, and compare that to the Floating God's choice. Then I could base my character choices on this outcome.
For example. The Floating God is going to take Yellow next, and the three colors upon health loss is Red,Green,Yellow. I can tell by my health and the playfield that I'm going to be hit twice as mentioned. My personal strategy is to use strong guys first. So, the Floating God takes my current Yellow guy, and I'm given my two choices -- I pick the weaker guy, because I know the next Yellow guy is about to be taken right away, and I don't want to waste a strong guy for only 1 or 2 turns.
Now comes the game bug. After the Floating God takes my Yellow guy, the "3 chosen" resets! If I'm lucky it will still be choosing the Yellow guy up next, but I've had it happen more than once where that wasn't the case. It went from Red,Green,Yellow to Red,Green,Purple for instance.
I think the game needs to keep the "3 chosen" consistent. Regardless if the Floating God takes someone, or if its inbetween full rounds, they need to stay the same. This would allow us players some more strategy.