Cardio does help out but so does nutrition and other factors. It's all about what you are eating and portion sizes. You can still eat out and be healthy, you just have to make healthy choices.
I'm sure the running will help…it's good for your heart! :)
Just cutting the soda out of your diet you will see some resold but it will take longer. If you want best results watch what you eat. Find low cal food. Diet soda will not work. You also want to include resistance training as well. For me I do cardio, resistance training and diet. I have been loosing 1-3 lbs per week.
I suggest... eat food but not oily and take more water because it's gives you vitamin and do daily exercise at home by using equipment like treadmills, cycling and many more....