Everyone's body is different, and there's so many variables: age, fitness level, etc., so the sugar thing may work for some people and not be noticeable to you. Personally, FWIW, I had a bit of a weight problem ~12 years ago, and I was drinking soda a lot every day. I cut out the soda, among other things, and no longer have a weight problem. I attribute much of it to the sodas; there's a lot of calories there, and no fiber (as in fruit) to help you moderate it.
The gluten free diet isn't likely to help you at all unless you have a problem with gluten. Gluten-free foods are NOT healthier (in fact, quite possible the opposite, to a small extent, according to recent research). The only reason to eat GF food is because you have Crohn's disease or some other gluten intolerance, which affects I believe about 5% of the population or so. If you don't have any of these problems, then stick with gluten.
Vegan diets are not healthier. The main reason people adopt these is because they don't believe animals should be used for food, including animal products (eggs, milk, cheese, etc.). It's not for health. Of course, too many eggs isn't healthy either, so you might get some side-effect here, depending on what animal products you were eating before and how much, but this isn't the goal of veganism, it's all about an extreme view of using animals and their products as human food. If you think that meat is bad for you (which again isn't scientifically supported; we're omnivores), you can always just adopt a vegetarian diet. Or, if you think you're eating too much red meat (which is a common problem with Americans), you can always just eat less of it, instead of adopting an extreme diet.
It sounds to me like you're young (under 30) and healthy, so of course you're not going to notice any difference with various diets unless they're cutting out something you really need or not supplying you enough calories.