If we are talking about someone from the UK, it's my understanding that until recently, a married woman had to put her husband as the father of any child - regardless of what the truth was or not.
As to how you find out who the biological father of various children was, it's potentially possible to construct a DNA tree, but that relies on you have the co-operation of any dependents, plus it's expensive.
Another option that might be possible is to get the military records of when your GG Grandfather was in the forces, and work out where he was and when - which I think might be possible. If he was abroad, and not on leave, when some children were conceived, then you at least know that he wasn't the father of certain children.
Of course, that doesn't tell you who the actual biological father was.
With the help of a military expert, I was able to do this with one of my relatives - he was not the father as he was in India at the time, and not at a level which allowed people to go on leave. Still haven't found out who the actual father was.
EDIT: I just thought, if the names are crossed out, that does suggest that at some point the 'truth' was revealed to someone in authority? Have you checked the newspapers to see if there were any legal cases about your relatives? Something might possibly come out there.