Are Ideal Greenie 30-192P Ground Wire Nuts approved for use with stranded wire?
The deciding factor is whether the device is listed (survives UL etc. testing) for that use.  The conventions for listings are as follows. 


If it says "12 AWG", it is listed for both solid and stranded wire.  
If it says "12 AWG SOLID" that means it is not listed for stranded wire.


So, if you have found where it specifies such things, and it is not specific as to solid/stranded, that means both.