What is the purpose for two nitrogen charged chambers in an oleo strut?
Two chambers at different pressures creates a variable rate spring. Initial landing shock is absorbed by the low pressure chamber until its nitrogen is compressed to that of the higher pressure chamber, which then has sufficient volume to allow the desired amount of further compression at the higher pressure. The lower pressure chamber would have already consumed virtually all its volume. 

The illustration is somewhat misleading in that the floating piston in the high pressure chamber should appear bottomed out when the strut is extended. There is no way for a fluid to be in equilibrium at two different pressures.