In response to jmcalli2 post#38,
Shortround6 gave what may be the entire answer to the P-38's large radiators in his post#39. Since the P-38, P-39, and P-40 engines were all designed around the 2/98 coolant mix, and originally had about the same power output, the basic cooling parameters would be the same except for the effective operating altitudes.
The only reason this might not be the entire answer is the different design concepts and understanding of the physics of cooling at the time. In other words, some designers/systems were more skilled/efficient than others. A well designed liquid cooled system for large high-power engines would, everything else being equal, be more compact (but probably heavier) than an air cooled system. And obviously, a less skilled designer might simply come up with a less efficient system.
As to the design concepts, the size related cooling effect of radiators is somewhat proportional to the overall frontal area x the depth of the cooling tube/fin array.
Everything else being equal, a deeper radiator can be more efficient at high air flow speed than a large frontal area radiator, and a radiator with a large frontal area will be more efficient at low air flow speed. But the larger the frontal area the more cross sectional drag in comparison to a deeper radiator, to a limit. There will be a balance between the volume available for installation, the overall drag of the radiator, the efficiency of the radiator, and the design speed of the aircraft.
In the time period we are talking about, much of the knowledge was based on trial and error for new designs, some were simply a carry over from older designs scaled to hopefully meet the new design requirements. The cooling system on the P-51 was one of the first designs to incorporate a mature understanding of the Meredith effect. (Interestingly enough, the cooling system on the Hurricane made use of the Meredith effect also, just not as efficiently.)
Sometimes the reason for a less efficient system might be as simple as avoiding patent infringement.
As for the oil coolers, most of the above answer applies also. The only additional significant factor I can think of is just how much the designers wanted to rely on the oil cooling system to also help cool the rest of the engine. The more cooling by the oil coolers desired, the larger the oil cooler radiators.