I have made some tests with my self-scanned objects. Not all work for a volume measurement with MeshLab. Important is during uploading in MeshLab that no warning occurs.
Simply download, for a test, the fine working DAVID OBJ angel (see the attached screen dump).http://www.david-3d.com/?section=Downloads
Result in cubic millimeter.
Edit. Some time ago I scanned a small elephant, carved of teakwood:viewtopic.php?f=6&t=4291&p=27756#p27756
Weight: 76.5 grams
Specific gravity of teakwood: 0.64 gram per cubic centimeter
So its volume should be 119.5 cubic centimeter
Volume result from MeshLab: 122.8 cubic centimeter. Difference 2.7%.