Here is a tutorial on the basics of running Unity inside of a normal Android app.
There is a great tutorial on running Unity inside of Android Views. Once you get this up and running you can start embedding scenes easily anywhere in your App.
When you need to call into the Java Android app from Unity, you can add this code:
AndroidJavaClass unityPlayer = new AndroidJavaClass("com.unity3d.player.UnityPlayer");
AndroidJavaObject activity = unityPlayer.GetStatic<AndroidJavaObject>("currentActivity");
And then you can call any method you want on your activity through the activity AndroidJavaObject. Something like this:
activity.Call("yourFunctionName", parameters);