Does the functionality of email forwarding from an old address to a new one exist

You have listed the three reasons, so it's good that you are aware of them... Let's go through them:

1. Hacking

   You handled this just fine by quickly changing your password.

2. Spoofing

   The SMTP protocol (the connection used to send mails) allows anyone to specify the address the mail originates from. So for instance, I could send a mail from any Yahoo address without knowing any password, it's possible but it's illegal...

   Most of the times, you can't do much against spam but if it's keep happening you can at least try to identify where the mails are coming from. You can do this by requesting someone who received your mail to check the mail headers and send you the data that is in there.

   This allows you to inspect the IP/host it comes from and inform their ISP about the spam.

3. Malware explosion

   You handled this just fine by verifying the computer is clean.

There's nothing that you can do. If the spam is actually being sent from that Yahoo! account, you could change the password (but since you said that you "can not control", you may not have access to the account anymore)

Most likely a spammer has retrieved the address book and the From address, and they can easily send messages with a forged From address (or send them directly through the Yahoo! account if they control it). The cat's out of the bag at this point. You can't stop the messages. All you can do is warn your contacts to ignore them.

You could try to recover the password to the Yahoo! account if you know the recovery information. Use the "Forgot password" link on their site.

The spam may not even be coming from Yahoo! (if your account was disabled, it certainly couldn't be coming from there, unless someone else registered a new account using your old disabled name). It's trivial to forge the From address on an e-mail address.

If you have one of the emails you should look at the message headers (how to depends on the receiving client or service) to see if it actually originated from Yahoo!'s servers.

In future, make sure you have a strong password on your e-mail accounts to prevent them from being broken into and having the contacts list stolen (or e-mails sent in your name.)