Place it in a graduated cylinder (or any other metered container), completely submerge the object, and record the amount of water displaced.
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Place an empty beaker onto a second larger catch pan. Be sure that your catch pan will hold water without leaking, and make sure it is large enough to catch ALL of the water that will spill out of the beaker. Fill a beaker until you can see the meniscus above the rim of the container. CAREFULLY lower your irregular object into the beaker with water allowing the beaker to over flow into the catch pan. Once you have your object submerged in the beaker, remove the beaker from the catch pan. Let the little bit of water adhered to the exterior of the beaker drip into the catch pan for a few seconds to make your measurement as accurate as possible. Using a graduated cylinder, measure the volume of water that has over flowed into your catch pan. The volume of this water will be very close to the volume of your irregular object.
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If the object is irregular the best way is to measure the volume of water it displaces when you immerse it completely in water.
If you push it down, you can measure the volume of the displaced liquid.
I would place it in a container full of liquid after measuring the liquid. I would measure the amount of liquid displaced by the object. That amount is equal to the volume of the irregular object if it is fully submerged in the liquid.
Put the object in a measuring container; pour in water to cover the object and measure the volume in the container; take the object out of container and measure the volume remaining. The difference is the volume of the object. If the object floats push it down until covered with water.
If possible, fully immerse the object in water, and measure the volume of displaced water.