From which bouldering and climbing grades do you start using Campus Boards, Hang Boards and Peg Boards for training?
As the comments have mentioned, grades vary somewhat between gyms, but I think you can still provide some rough guidelines.
Peg boards can probably be done by anyone at any climbing level. You're not stressing your fingers really, so there's little chance of injury. It's essentially like practicing pull-ups. It probably won't help your climbing too much (except for lock-off moves).
You should be at least a solid V4-5 climber to start hangboarding. You should be able to do crimpy climbs at that grade range, since that is basically what hangboarding is. If you can hold onto a hangboard grip >15 seconds, you're probably not stressing your fingers too much (thus, relatively safe). But make sure to take it easy at first and stop at the first sign of pain. Also, make sure to take at least a day off between hangboard workouts.
For hangboarding, you could start even earlier if you wear a harness and attach a weight on the other side of a pulley system to take weight off your fingers.
Campusing is more intense on fingers than hangboarding, so you should probably be a solid V6 climber to start. Again, you should be able to do crimpy climbs rated V6+.