Example: I traded to a friend and I had no gym badges and my friend had a lvl100 mewtwo in a luxury ball... will the mewtwo obey me if it is in a luxury ball but I have no badges?
No. The Luxury ball only increases the amount of happiness gained by the Pokemon towards you. As it was traded to you, you will have to get the badge that causes all Pokemon to obey you. Normally the eighth badge.
Nope you have no badges it wont obey you until you get all 8
Get the eight badge and it will fully obey you.
Right now it won't always.
It will Not obey you
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