Sugar is a needed and necessary nutrient for our bodies. But, much like anything else, the poison is in the dose. For example, our bodies are mostly made up of water. Good old H2O, necessary for all life on Earth. But drink too much water in too short an amount of time and you can die from electrolyte imbalance. By and large it's the dose, not the substance that is poisonous.
Our bodies were designed to take in small amounts of natural sugars from fruits and vegetables. Large amounts of sugars will, as you said, be converted to fat. and can make you lethargic and ill-feeling.
Ironically, (at least in the US) Most soft drinks and other "sugary" foods don't actually have any sugar in them. Instead they use a far more dangerous substance, High Fructose Corn Syrup, or HFCS.
HFCS is a cheap (due to corn subsidies) easy to transport, slow to spoil, and highly soluble in water, making it an ideal sugar substitute for much of the food industry. The downside is that HFCS in any significant amount causes the human body to react in some very adverse ways. HFCS causes thirst, liver damage, diabetes and as has been recently discovered by researchers at Princeton University causes extreme weight gain and obesity far in excess of what simple sugar can do. In particular, HFCS causes weight gain in the belly and torso. HFCS also causes significant increases in the amount of triglycerides in the bloodstream, a major factor in heart disease, the number one killer of adults in the US.
So it's good that you are cutting out the soft drinks and other "sugary" things, but unless you live somewhere that doesn't use HFCS (South America, parts of Europe, China) make sure you are blaming the right thing. otherwise, i think your diet change is a sound one. Lots of fresh meats, fresh vegetables, small amounts of fruit and grains and an absolute minimum of "sweet snacks". (This is basically the "maintenance" portion of the Atkins diet, btw.)
Also, if you live in the US, be sure to join a group lobbying for the repeal of corn subsidies of all kinds. It's the subsidies that make HFCS so cheap. eliminate them, and the food industry will go back to using much more benign sugar.