Lateral Motion Devices

How did these devices work for the rods, to allow tighter curve radii? The rods have to be a fixed length between each drive length.

There may have been such devices installed commonly, but I am not aware of anything other than the standard bushings and couplings which may have had lateral play. I do know that often times, a multi-wheeled engine would have flangeless wheels, mid-point in the drivers, at which point the wheels inner edges would overide the inside of the running rails on curves. (just like Lionel) Other than articulation and the fact that railway wheels are conically shaped to allow the inside wheels to slide towards that side on a curve, compensating for RPM differences, I am not aware of any other built-in compensator.

There is no compensator.
All rods had a lateral plan and there were only a few realy fixed.
That made working with roller bearings difficult, because lateral play had here to be different.

Also the axles had often radial play, just to ensure that they were able to adjust in curves, and special radial or curve control mechanism were developed, like the Kraus-Helmholtz-steering-truck or the Schwartzkopff-Eckhardt-truck were found in Germany, to help the locomotives, to move much better through narrow radiis.
So the well known series 50 or the war type 52 series stema locomotive hat a Kraus-Helmholtz leading truck.

The absence of a flange on several wheels made it often a problem on very narrowly curves, that the engines derail with those wheels... surely, they themself railed-in after the curve or a switch, but those wheels often badly damaged the tracks, so this was quickly abandoned in Germany, with their very narrow curve radii on their railroads.
So here those steering trucks and the better lateral play of axles and rods fixed that problem, and later on roller bearings, special develpments were done, to ensure that lateral play, without any stress to the bearings or rods.
Most famous is the SKF pendulum roller bearing...