The following lived circa 1920 and onward with their mother Mary in San Jose, Santa Clara, California:
* Mary M O'Conner b Oct 1880 CA (gone from home by 1920)
* Nellie C O'Conner b Mar 1883 CA (gone from home by 1930)
* Jennie/Jane F O'Conner b Aug 1884 CA (gone by 1930)
* Annie T O'Conner b Aug 1886 CA (still at home 1930)
* James O'Conner b July 1888 CA (still at home 1930)
I think the above list is the group you know the least about - but I can't tell for sure, because I can't check all your past internet postings. Check your own records, prioritize your goals, and help us focus on the first person you wish to find by providing as much detail as you can.
In the past, in other threads, you've been asked to supply more detail and then you didn't. You responded with another question. Boy do I get that - we're so focused on our search and on what we want to find out, that we forget how important it is to inform collaborators of what is known so far. And I'm not the only one who gets it. Tons of people who post genealogy queries do the same thing.
But I hope you won't do that here.
Think of writing a query as if it is like prepping a room to be painted. By the time you shop for your paint and brushes, move out the furniture, cover things with plastic, tape the windows, haul in the ladder from the garage, and gather rags and clean-up supplies, you've spent a lot of time getting ready. The actual painting takes far less time. But you know the prep is hugely important, and it is not a separate job - it is part of the job of painting the room.
Know that my comments are not personal to you. This problem comes up so often. I do wish all of us in the genealogy community did a better job of setting up query writers for success.