Sugar with vegetable oil safe

Oil doesn't really dissolve sugar. The main purpose for the mixing is that in many recipe techniques, especially the muffin method, sugar is treated as a wet ingredient. By premixing the wet ingredients, and premixing the dry ingredients, when the two are combined, you require much less additional mixing to get a homogeneous total batter.

Creaming sugar into butter or shortening helps leavening because the sharp edges of the sugar crystals cut air into the solid fat medium, essentially creating a foam. This then serves as seed air bubbles for the chemical leavening to expand. This effect cannot occur with liquid oils.

Many carrot cakes are pretty dense and oily, although I don't think they should drip when pressed. You might have something else going on in your recipes or technique.

See this article from Colorado University Safe Food. The goal is to prevent growth of the botulism pathogen. Here are their key points:

• Wash all soil-contaminated produce before adding it to an oil infusion,
• Add an acidifying agent such as lemon juice or vinegar to the recipe at the rate of one tablespoon per cup of oil,
• Keep oil infusions refrigerated in order to retard the growth of any microbes,
• Discard infusions after one week, or sooner if apparent cloudiness, gas bubbles, or foul odor develop and,
• When in doubt, throw it out.

Sorry the source article is not formatted prettily, but I was looking for something more authoritative than about.com or ehow.com.