none of the above will cause a problem as they are all clear liquids. Milk, although not clear, would be so diluted with other liquids, would never do it either.
A grease trap is the 'U' shaped pipe directly below your sink with usually a screw off cap on the bottom.
Just incase your Aunt Tilly drops her diamond ring into the drain. It should stay in the trap and you can open the little cap and get it out.
Edit, SLOB, I think, even if he had a garden, animal fats would NOT be a good idea. Would attract too much unwelcomed life forms.