The more muscle mass you have, the faster you will burn fat. This is precisely why men lose weight faster than women do: they have a greater percentage of muscle mass vs fat on their bodies. So, that right there works in your favor.
Now, you're already lifting weights, which will help build more muscle. Make sure you strength train only every other day; your muscles need a day to relax and repair. You're also doing a decent amount of daily cardio. This is great and is the best way to burn fat. You're really giving your body the one-two punch. But the question is, are you doing it at the right intensity? You need vigorous exercise in order to lose weight. Build up a sweat, check that your heart-rate is in its target zone, and try to talk while you're working out. If you have trouble talking (without feeling like you're going to keel over), then you're doing it at the right intensity.
The only thing left is your diet. There is no need to give up meat OR carbs. In fact, your body absolutely needs both protein and carbs. (Protein for the building and repair of muscle tissue, as well as stamina; carbs for proper brain function and essential quick-energy.) What's important is the TYPE of each you are eating.
Examples of healthy proteins:
pinto and black beans
lean meats (chicken, turkey, fish, venison, buffalo, and if you must, beef with all visible fat trimmed off)
low-fat cottage cheese
low-fat yogurt (non-sweetened)
Examples of complex (or good) carbohydrates:
whole grains: 100% whole wheat, rolled oats, brown rice, buckwheat, whole barley, oat bran
fruit: apples, dried apricots, strawberries, oranges, grapefruit, pears, plums
vegetables: carrots, sweet potatoes, broccoli, spinach, tomatoes, eggplant, cauliflower, zucchini, asparagus
legumes: lentils, pinto beans, soybeans, garbanzo beans, kidney beans, navy beans, black beans, split peas
dairy: low-fat yogurt, skim milk
Examples of simple (or bad) carbs:
corn syrup (and anything that contains it)
fruit juice (unless it's 100% pure juice NOT from concentrate)
most packaged cereals (esp. Those with added sugars)
all baked goods made with white flour
and pretty much most desserts and pastries
It's good you're not drinking soda. That's like public-enemy #1 when it comes to weight loss. The other thing I just thought of is are you eating enough?? This sounds a bit daft, at first. But the truth is if you're exercising like crazy but not fueling your body with the proper amount of calories, then your body goes into a sort-of starvation mode state. It will actually STOP losing weight and hold onto whatever fat reserves you have. Talk to your doctor. Get a physical and ask him what is the proper amount of calories for someone your age, weight and height. You didn't mention your height so I can't tell you what is proper for you.
As for your belly and excessive chest, shall we say… Sadly, there's no way to "spot-reduce" any part of your body. You can only burn fat over all of your body, and do specific exercises to tone muscle in the parts you want tightened. So, do daily crunches, making sure to work the obliques (the side abs), as well. Do bench-presses, rowing, and similar weight lifts to work your pecs. Once you start to lose the fat, the muscle you begin to develop will start showing through, giving you the overall tone you desire.
Good luck to you. You're doing a great job so far. Keep it up!