My favorite turn based RPGs on Android so far:
Cthulhu Saves the World
Penny Arcade's Rain Slick 3
Avadon: The Black Fortress (tablet only)
They all have good storylines with solid writing (not cheesy poor translations), are Android ports of PC games from indie developers, and are completely free of IAP.
Edit: I forgot to mention that Avadon was just added into the current Humble Bundle for Android for those who pay higher than current average. Check out humblebundle.com.