The simple solution is to just move the joins a lot, the plastic will wear down with use. This is why mini-figures that little kids have played with for years are just downright floppy.
Zhaph gives some good advice about oils, watch out for stuff that is hydrocarbon based as this might also be act as a solvent. I want to say that silicone based lubricants might be the thing that could work for you. I recall someone talking about using it for some technic axles awhile back. You might do some google research on this topic.
If you remove arms, be careful, as torsos can develop stress cracks along the bottom edge that will split up to the arms. These are not repairable, and ruin the torso.
Finally, if you want to FIX loose Lego figure arms, legs, heads, etc. I have a very solid and simple fix that I have used many times over the years. Take a VERY tiny drop of crazy glue and put it inside the joint, and let it dry overnight. This will cause the joint to be come ever so slightly smaller, and it will make the joint nice and tight. It is inside the joint, so it is completely invisible, and if needed it could be done repeatedly.
But be very careful, as crazy glue will mark Lego it drips on. Let it dry for a long time, so you don't accidentally glue the joint together. And finally, just to repeat, a VERY small amount of glue. It doesn't take much at all.