Is there a way to move an endpoint from one Organization or Case to another?

Moving an asset (aka Endpoint) from one Organization to another is prohibited.

Organization assignment is performed on the installation of the AIR agent process, and assets are directly bonded to the associated Organization. So there is no way to directly move an endpoint from one Organization to another. If you want to move an endpoint from one Organization, you must uninstall the agent from the asset, and then you must create a new agent deployment package and must select the Organization you want.

Moving an asset (aka Endpoint) directly from one Case to another is not a valid action.

Actually, assets (aka Endpoints) are not directly attached to Cases. They attach to a Case via a Task. When the Tasks of the endpoints are added to the Cases, the endpoints appear in the Case. An endpoint can be included in more than one Case. When you add the endpoint's Tasks to different Cases, the endpoint appears in those Cases. You can add Tasks to a Case or send a completed Task to other Cases with the "Send to case" action.

If you remove all the Tasks of the endpoint from the Case, the endpoint will be removed. You can directly remove the endpoint from the Case. This way, all its Tasks will be removed from the Case. Then you can add Tasks in interest to any Case you want.