|Are you using web based email (such as hotmail, yahoo) or mail ralay software (such as outlook)?|
If you're using web based email I'd suggest just changing your password and sending a detailed report of the problem to your web mail provider.
If you are using mail relay software, is it doing it when your software is on or whenever? That makes the difference on whether the problem is on the mail server or in your mail client. First thing you chould try is to change to another sofware. If you're using Outlook, try running Thunderbird only for a while instead and see if it's still doing it, If it's not doing it anymore, at least you have neutralized the problem for now. Then get a free antivirus (Avira, Avast and AVG are popular choices) and do a full disk scan.
Important note: If changing your mail client works, do not open ANY of the infected emails you could have in your account. Delete them permanently.
If you are using a mail relay client but it is sending spam mail when your computer is off, then the problem is most likely in the mail server. Contact your mail service provider and report the problem with details.
Changing your password may be helpful in any situation depending on where the virus is working from.