[Duugu]

Pass a reference to the object with DropDownMenuItem_OnClick. Example:

f = CreateFrame("MyNewFrame")
DropDownMenuItem_OnClick(f)

Then add a parmeter to the function and use it within the function:

function DropDownMenuItem_OnClick(self)
    UIDropDownMenu_SetSelectedValue(self.owner, self.value);
	PlaySound("igMainMenuOptionCheckBoxOn");
  if (self.value == 0) then
    --We clicked the first menu item. Enter code here to affect the rest of your mod.
  elseif (this.value == 1) then
    --We clicked the second menu item. Enter code here to affect the rest of your mod.
  end
end

[Edit]
LUA isn't OOP.