If you are dealing with a true oil-bath air cleaner, they use a pool of oil in the bottom the air cleaner pan. The mesh above the pool should be wetted with oil, but it is mostly a 'bug catcher.' The actual dirt capturing takes place by the change in direction of the air flow, from down to up, that takes place above the oil pool. Dust, etc. contained in the incoming air has a higher inertia than the air itself, so the incoming dust dives, so to speak, into the oil. Oil bath air cleaners have a slightly higher pressure drop than do paper elements because of the reversal of the air path, but for applications other than in racing engines, the difference is insignificant. Oil bath air cleaners have to be cleaned every couple of thousand miles or so, depending on operating conditions, but do not fill the oil pan above the "fill" level. Usually, there is a mark or arrow indicating the full level, but if not, typically there is a rim a little way above the bottom of the pan that is the 'fill' level. The OEM air cleaners are marked pretty clearly. If you put too much oil in the pan, you risk pulling oil into the engine and having a lot of smoke- or worse.
Also, use a fairly heavy oil in the air cleaner pan; SAE 30 was typical in the past, but a heavier grade is alright. Light/thin oil may be pulled out of the pan by high air flow.
Paper filter elements typically are a little better at capturing small particles, but oil-bath air cleaners did a good job when maintained properly.
Harvester