I haven't done any reading on Body by Vi, but the Military Diet (also known as the 3-day diet), is really just a very low calorie diet that is unsustainable for long-term. You might lose 5lbs, but it will be of water weight, not fat, and you will most likely gain that back within a day or two of regular eating (It's fine if you need to lose a little weight to fit into a dress or something for a night, but not for actual weight loss).
If you want something long-term that will have you losing weight steadily and healthily, you can do low-calorie and still incorporate the things you enjoy (I believe another member, JohnP, has this in his signature "I eat what I want, just not as much as I want"). Low-calorie diets can be accomplished using an App/Website (LoseIt, Myfitnesspal, etc), there are books you can carry in a purse (Calorie King), or you can simply use a web browser to google the calories of a specific item and write it in a journal.
Take a look through the forums here, there is tons of helpful information that I'm sure will help!!