Mouthfeel is really what it says. Does the wine fill the mouth? Is the wine built like a 'skyscraper', to use a Parker term, with many layers of taste and very thick, or much more linear, running just over the tongue?
Structure is more difficult to define. It refers to the balance of different aspects, such as fruit, acidity, tannins and alcohol. A positive perception is an indication of improvement potential over time and ability to age.
Texture is often used interchangably with structure. I often use it more specifically to describe the tactile sensation experienced as a result of acidity, tannins, and residual sugar. In great wine, I often think of texture first, rather than aroma.
Maybe this helps with some of the terminology.