In order to determine if a compound is polar, nonpolar, or ionic, we need to look at the main component of this compound and see the difference in the electronegativity between the elements, if the difference (which can be easily found in many tables online) between the electronegativity if high, then we have an ionic compound, if it is very low, then we have a nonpolar compound, if it falls in the middle, we have a polar compound.
For water, we have H and O, which are not high to be an ionic compound and not low enough to be nonpolar, as water is known the best polar solvent, water is a polar compound
Acetic acid is the main component of vinegar, and since it is an acid, it is also a polar substance and has a high solubility in water
Iodine solution is classified as nonpolar due to its concentration of elemental iodine, and it is better dissolved in oil
Alcohol substances are made with the same type of components as water, O and H, which also makes it polar
Vegetable oil, as an oil it is nonpolar, most oils are nonpolar
Therefore we have:
Water - polar
Vinegar - polar
Iodine - nonpolar
Alcohol - polar
Vegetable oil - nonpolar