Elizabeth I don't know of any sure way to distinguish between later (water) and alkyd (oil) based paints once they have dried on your walls, but a few guidelines.
If the paint is over 20 years old, its usually oil If it is in a kitchen or bath and its gloss, its often oil. If it has small check-marks or lizard-skin appearance, its oil If it chalks (usually exterior paint) then its oil. You can tell this by wiping your hand over the painted surface...if the color comes off on your hand as a light powder, then it is chalking.
These are from my experience. Another source you can check and even ask questions is the Paint Quality Institute at http://www.paintquality.com/