I would use the ruler on my Swisschamp to measure the inside diameter of the container and the depth of the liquid therein, and use that to calculate the volume.
Or, use the ruler and other tools to make a smaller measuring cup from materials at hand, and use that to measure the liquid. For example, if you found a piece of pipe with a 2 inch ID, you could close one end with wood, duct tape or whatever, and use the saw to trim it to a depth of about 2-1/5 inches. That would give you a measuring cup of about 4 ounces, or 1/2 cup. In fact if you had some duct tape, you could make a cup entirely out of tape. Saw a flat end on a stick and whittle it to a known diameter (e.g. 2 inches) and use that as a former. Wrap the tale around the stick with the sticky side out, then wrap several additional layers with the sticky side in. Slip it off the former when done.
Or, you could even carve the classic bushcraft dipper/cup out of wood. Use the saw and the main blade to form the outside to the shape you want, then the small blade and the chisel to carve out a cavity. Use the ruler to calculate the volume of the cavity.
ETA: As an experiment, I just used the fish scaler/ruler on my Swisschamp to measure the interior volume of a Beanie Weenies can. I calculated it as 0.92 cup to the lip, so I figured it would be approximately a cup if I filled it to the absolute top. So I filled it completely full of water, dumped the water in a measuring cup, and it measured right at one cup.