As long as I can remember there has been debate on how to clean and lubricate axles. With or without grease? And if yes, what to grease and what not? Thru the years I have found my way, partially guided by the knowledge past on by my father and an engineering degree but even more so by common sense and a fetish for clean gear.
Much debated as a lubricant it does a superb job as cleaning agent.
Ok let's dive right in... Important to know is that the axle in your Bicycle or Walking Trailer is not the part that actually turns. For some this will be a complete surprise but it is so. You can experience this by holding the axle in at the end while inserted in the wheel. The axle does not turn when your spin the wheel. The part that turns is the bearing inside the wheelhub (see picture).
This is important to acknowledge because it means we don't have to grease the axle for that reason.
Some suggest that you should still grease the axles against rust. My experience though is that grease is sticky and attracts dirt that leads to "gunk" that leads to more sand and dirt that leads to problems that are messy (and greasy) to clean and solve. Personally, I believe in crispy clean axles.
I start by taking the axles out of the wheel. Then, I spray WD-40 on the axleshaft, at the button-side, and in the ball holes at the end of the axle. Just WD-40 them completely and use an old rag to wipe off all the dirt and finally the excess oil. This way the axles are really clean and have a very thin oily coating. I would recommend to do this for every longer period the trailers sits without use or every week at least on a long walk or whenever you take of the wheels. Don't worry if the axles are dirty, that is the nice thing about WD-40, it cleans extremely well and leaves a little oily coating afterwards. You can also get it everywhere around the world for a very modest price.
The bearings inside the wheels should not be cleaned with WD-40 as they contain grease and WD-40 sprayed there would clean out the grease from inside the bearings
The bearings are best cleaned with a rag with some WD-40 sprayed on the rag. Cleaning
wheels and spokes also works very well with WD-40.
Clean the Axles while out of the wheel with WD-40 thoroughly and use a rag (with some WD-40 on it) to wipe the wheels, spokes, hub and bearings inside the wheel hub.
This way your trailer will serve you well for a long period with much less risk of problems. And if problems do occur you (or a local shop) will be happy not to have to work on a greasy, gunked-up mess.