Some people above mentioned that the only thing that matters is calories in vs calories out.Thats not true.Anyways first things first.
Vegetables should play the big part of your diet.Why cant you eat them?have you tried talking with doctor, nutritionist?Is it something more serious than childish stubbornness?
All diets have you eat veggies for two reasons.#1 it makes you full.#2 Its has lots of vitamins , that you will be likely not getting enough while on a diet.
You have mentioned that you eat junk food, drink soda.In other words , you should fix your eating habits first, before diving in caloric deficit.Start eating healthy, unprocessed, whole food.When you will have your habits fixed, you can start playing around with calories.Find your maintainance levels and cut 300-500 from that number.This will be your starting point.Start weighting yourself.You should be losing 1 pound per week, however you can aim for 2lbs/week.IF you stop losing weight, just reduce caloric intake, however keep your fat/protein/carbs precentage the same.I recommend 40/30/30 ratio of protein/carbs/fat.You can increase carbs and decrease fat on workout days and vica versa on rest days.
GOod luck, if you have any questions feel free to ask.