When your contract terms are completed. You may be able to go 1 week early, but Verizon no longer allows early upgrades. Occasionally you can be offered early edge upgrade where you turn in your current phone and are allowed a promotional phone that Verizon chooses. This must be offered to you.
Depends on when you started Edge, but current Edge allows you to Edge up once you have paid off 75% of your current phone.
Off any type of contract: Anytime.