Problem

Outlook cannot handle outbound mail. One or more of the following appears in the atlassian-jira.log:

javax.mail.SendFailedException: Invalid Addresses;
  nested exception is:
	class com.sun.mail.smtp.SMTPAddressFailedException: 550 5.7.1 Unable to relay for jira@google.com

com.atlassian.mail.MailException: com.sun.mail.smtp.SMTPSendFailedException: 550 5.7.1 Command not allowed

com.atlassian.mail.MailException: javax.mail.SendFailedException: Invalid Addresses;
  nested exception is:
	com.sun.mail.smtp.SMTPAddressFailedException: 554 5.7.1 <user@mail.com>: Relay access denied

Caused by: com.sun.mail.smtp.SMTPSendFailedException: 550 5.7.1 Client does not have permissions to send as this sender

 There is a known bug tracked in  JRA-31238 - Getting issue details... STATUS  which has been verified to affect instances where the project level From address is configured to be different from the global SMTP From address in JIRA applications.

Cause

Your Exchange mail server is not configured to relay messages. 

Resolution

Exchange 2003:

Open the Exchange System Manager

1. Go in Administrative Groups -> Administrative group name -> Server -> Server name -> Protocols -> SMTP
2. Right click on Default SMTP Virtual Server -> properties
3. Access tab -> Relay button
4. Select "only the list below" and add the domain and\or IPs of your server

Exchange 2007:

For Exchange 2007, create a second receive connector for external addresses as described in How to Set Up SMTP Relay in Exchange 2007.

Check Microsoft's Exchange Archive as well.

Office 365:

Take a look at Microsoft's documentation on how to set up permissions for relaying messages in Exchange.