...
You can then create New Query, typically e.g. "Assigned to me (All Projects)", and open JIRA issues straight in Eclipse, update them, attach Task context to them - use Mylyn!
FYI: EGit integration for Mylyn is being actively worked on.
PS: Page written up upon discovery that this appears to basically work; hasn't been extensively tested, yet. Mylyn was known to have issues with (highly) customized JIRA instances (e.g. used to be unable to handle custom workflows), but as mifosforge.jira.com is relatively standard (and Mylyn made progress), should be OK? Please do not hesitate to update this page with further findings.