Which unit is best for expressing the volume of an irregular solid?

The fact that a solid is irregular has nothing

to do with which unit you pick. It is the size of the object which

determines this. If it is the size of a room you might use metres

cubed, but if it would fit in your pocket then centimetres cubed

will be more appropriate. It is the method of measuring the volume

which is affected by the irregularity. You can't do it with

measuring and geometry, so you have to use the displacement of

water.