The trading team was disbanded. Is this sentence idiomatic?

Your suggestions are all acceptable, but "disbanded" or "broken up" seem most likely. "Dispersed" suggests that the team members were actually sent to different physical locations.

In the actual example, do you need to say that the team was disbanded? If the team members were all fired then the team must be broken up in the process. So the simplest way to say this:

The trading team made a big loss, so the team members were all fired.