Q: delete old device

Removing an associated device or computer from an Apple ID

To remove a device or computer from your Apple ID:

1. Open iTunes.
2. Sign in to your Apple ID by choosing Store > Sign In from the iTunes menu.
3. Choose Store > View My Account from the iTunes menu.
4. From the Account Information screen, click Manage Devices.
5. Click the Remove button next to the device name you would like to unassociate.

From >  http://support.apple.com/kb/HT4627

For iCloud, if you no longer have the phone (if you do then you can do Settings > iCloud > Delete Account on it) then try removing it via http://icloud.com - you will possibly need to send a remote wipe signal to remove the phone from your account (in which case all if the phone's content will be removed).

If your account is logged in on the phone then the only way to log out of it is to do it directly on the phone (e.g. tap on the id in Settings > iTunes & App Store), or remotely wiping the phone via the above may log you out.