Beat sugar and oil until smooth
The simple answer has to do with how things are dissolved in 
general.  When salt (NaCl) is placed in water, it "dissolves" because all 
the sodium ions and chloride ions separate from each other and "hide" 
(become dispersed) within the water molecules.  This is an example of an 
ionic system: Na+ and Cl- interact with the water molecules in a specific 
way...the positively charged Na+ is attracted to the part of water that is 
negatively charged and the negatively charged Cl- is attracted to the 
positive part of the water molecules.

Its the same general principle when talking about salt dissolving in 
vegetable oil.  Vegetable oil is made of lipids: chains of carbon and 
hydrogen, which are not ionic at all.  Therefore there are no places for 
the 
ionic sodium and chloride to hide within the lipids.  The Na+ and Cl- would 
prefer to stay with each other where they have nice ionic interactions..the 
result is that the salt does not dissolve.

Sugar, on the other hand, can have interactions with the lipids.  Sugar is 
composed of carbon, hydrogen and oxygen in a ring structure.  It has 
chemical groups that can interact with the CH's of the lipids AND it also 
has chemical groups (OH) that can interact with water molecules.  It 
makes contacts with the lipids and slowly starts to hide within the 
lipid molecules until its so dispersed that you cannot see it in 
granular form anymore.  Due to these properties, sugar can dissolve in both 
water and in the vegetable oil.