You can access your University email account in several ways:
You can also access incoming email from external providers. Ask your email provider for the details of their IMAP server or POP server.
To send email, ask your provider for the details of their SMTP server. If they have an SMTP server on port 587 or 465 you can use this from ResNet. If they only have an SMTP server on port 25 this isn't available from ResNet. Instead you should use the local University SMTP server.
Whichever server you use you can set up the From and Reply To addresses in your email program so that it appears to come from your external email account.