How is mass measured? Kilograms? It's important for my project, and I can't find any definitive answer right now… Thanks!
Densities used in the Material class seem to be based on grams per centimeter (just judging by what is there for Iron). Look at computeMass method of DynamicNode to see how the mass is calculated from density and volume of the shape.
You can define that for yourself. Have a look at e.g. the ODE manual on this topic.
I’m looking, but I can’t seem to find any function to define mass units. This is the document I’m looking at. Is it the right one?
You don't need a function for it. It's just a matter of thought 
- and about the dependency of speed, velocity, force and torque. And that's what you can find in that document (iirc, but it's general physics anyway).
That's very cryptic. Surely things like speed, torque, etc are calculated from the the mass of the object… not vice-versa?
Judging by the constant for gravity used OdePhysicsSpace, dimensions are in meters per second squared (default gravity [G] is set to -9.81f). So a dimension of 1f = 1 meter. Like I mentioned before, the default units used in the Materials class seems to be grams per cubic centimeter. I don't see anything specifically saying units are metric, but that seems to be what the constants are working out to.
Does this help? I may not be understanding your question correctly though.
So it's grams per cm^2? If that's so, that's great, I can work with that. I was hoping I would be able to set the mass of the object irrespective of it's size. Is there any way I could do this? I'm not actually using materials; I'm just setting the mass on dynamic physics nodes directly with setMass(), you see.