It's NOT wrong. It's just not common usage and it means something different from what you probably intend. We normally say we are "on the way home". The word "home" is flexible. It can be a noun, an adjective, or an adverb. Here are examples: NOUN: "I live in a home" ADJECTIVE: "This is my home address" ADVERB: "Let's go home", "I'm on my way home" The sentence "I am on the home way" is perfectly grammatical, but let's think about what it might mean. I would interpret "home" as an adjective modifying the noun "way". I would interpret "way" as synonym for "road". Thus, I would interpret "I am on the home way" to mean that I am on the specific road that leads to my house. That is quite different from the meaning of "I am on the way home". As long as I am driving towards home, I am on my way home, regardless what road I am on. However, I am only on the "home way" when I am on the specific road that goes to my house.

You are on the way TO a place. On the way TO the airport, on the way TO the restaurant. The only difference is that 'home' is an exception and the preposition 'to' is not used with. But you are still on the way to a place.

The most natural phrase is "I am on my way home". "I am on the way to home" as mentioned below is incorrect. We don't use the preposition 'to' for home. As for using 'the': we usually say, I am on the way. We don't add 'home' when you are using 'the' to be specific because in this context it means that you are currently in the process of traveling.

on the way to home