You can push it under water / under the liquid's surface, and measure the displacement of liquid.
Google "Archimedes' Principle" and see if that gives you a clue...
Finding the center of gravity of an irregularly shaped object can be done using the plumb line method.
Half fill a graduated glass beaker with water and note the level. Place irregularly shaped object into the beaker. Note the new level. The difference between the two levels is the volume of the object. cw: OK, that method works for objects that don't get wet -- like steel. Tissue paper would not be a good candidate. Also, if the object floats, you have to submerge the object.
the water displacement method
A beaker. Simply fill the beaker with a known quantity of liquid. Drop the object into the beaker, and measure the difference in the fluid levels.
Mass divided by Volume = Density. Or use the displacement method for an irregularly shaped object.
Asteroid
you would use the water displacement theory
If the object in question is water proof, and small enough. You can measure the amount of displaced water when it is placed in a tank full of water, this may not work for a lot of things but it can help when attempting to measure some objects.
Tight
Use volume displacement method.
Yes. It doesnt have to be a irregular even though sometimes it is easier just to do the math... for a rectangular object. l x w x h= volume