My ISP does not allow SMTP port 25 connections outside its network but only port 587. I don't use a desktop mail client like Outlook.
Can a virus still send spam mail from my computer? How?
I knew some key-loggers that uses default browser for sending email, the approach is called injection (Injection-to-browser) which allowed by firewall to connect to outside. SMTP is one of the method for sending email, however, the virus might use HTTP protocol to send the email for example: sending parameters to remote host (remote PHP page), then, the host uses your IP for hiding the spammer's IP.
Another Scenario: if the virus got a copy of your SMTP credentials, then it can use it from another PC (Outside your pc).
Yes. You do not need outlook to send an email, nor do you need a mail server - all you need is a connection to the Internet, a method of speaking tcp (telnet is one which comes with most PC's, but a virus would just hook into the TCP Stack using system calls), and knowledge of the public, and well understood mail protocol.
FWIW, any decent mail administrator can demonstrate how to do this - and most often has to to debug problems. (Un)fortunately sending an email is trivial, and requires nothing more then an Internet connection.
As far as your ISP's protections go, all a virus would need to do would be to discover the details of your ISP's mail server and "relay" mail through that server - just like outlook does. The advantage (to your ISP) is they can intercept the messages and check them for spam - and record the volumes, thus mitigating some of the risks.