I want to know which sentence is correct. "It destroyed everything in its path" or "It destroyed everything on its path"
It depends if the path is enclosed (like a tube) or open, assuming that you are talking about a monster rampaging through a city or something similar I think it is "On its path" to that. ON is used to denote a position for surfaces, in the situation of a city the path would be along the surface (of the ground). However you could also say that the objects are contained within the path.
This is where I got my information. http://www.differencebetween.net/language/difference-between-in-and-on/
In your sentences, "in its path" would be correct--it's a little more general. "On its path" would indicate a physical object physically positioned on top of a path (like a rock on a path through a forest).
There might be an island in the path of a hurricane, but the island can't be on the hurricane's path since there's not an actual path for it to be on.