The bottom line is that you will need to continue establishing a calorie deficit to lean out. There's no way around it - simple thermodynamics. Fasting is a great option because it naturally helps with calorie restriction, and has potential healthy benefits in it's own right, though this area of research is still pretty new. You should check out leangains.com, as the protocal outlined there is geared exactly towards your stated goals: fat loss while maintaining strength, or muscle gain with out fat gain using intermittent fasting.
The other bottom line is that getting much stronger while leaning out below 15% body fat is very, very difficult. I would recommend you focus on either fat loss or muscle gain one at a time. start counting calories and go for a daily deficit no larger than 500 kcal - anymore then that and increasing strength would be impossible. Keep focusing on heavy, compound lifts like squats and bench. Estimating your daily calorie expenditure is pretty easy with all the tools out there online.
People here might give me a lot of flak on this one, but I also recommend eating pretty carb heavy on lift days - you want to give your muscles all the precious glycogen replenishment they can get while you are eating at a calorie defecit. Check out the various posts on carb refeeds. Obviously if you have issues with diabetes or blood sugar, this might not be the best choice, though there are plenty of low GI carb sources out there such as squash and sweet potato. Eat higher fat on off days as it is more satiating. Don't skimp on protein either, get at least 1g per lb of body weight.
There's no magical food item or exercise gimmick that will magically transform you into Brad Pitt from fight club overnight... it just takes time and patience. It sounds like a lot of your gut may be loose skin left over from significant weight loss. I know nothing about that but there's plenty of posts on that topic on this forum.