I store my strikes in the long low coin boxes that are double rowed. As I have switched all my strikes to AirTite covers, I use the old covers as place keepers.
For my inventory, I have an Excel spreadsheet, which I obtained years ago from a fellow striker, listing all the strikes. I then fill in the info on when I bought it. I keep a paper record of my "finds", but this could all be added to the spreadsheet and kept in one place. I then make an extract worksheet of just those strikes I need. For the strike identification, I have been using Marv Weaver's original numbering and then updating this with Richard Anderson's catalogs. He publishes a great photo catalog update each year.
It sounds complicated, but really is not. I would be happy to share the Excel spread sheet to anyone who desires it.