Good morning Urooj,
Regarding SAML, I'm afraid that it is not supported. From the research that I have done I found out it is a common question, but the following link shows that this request is, at this moment, closed as "Won't Fix". https://jira.atlassian.com/browse/CWD-1822
On the bright side, Atlassian has a full team of experts (https://www.atlassian.com/resources/experts) who would be happy to work with you on custom solutions.
Regarding OpenID, there is also a request already created, but the status right now is Open. If you would like to check it out, here's the link: https://jira.atlassian.com/browse/JRA-13942
While this is not resolved, here goes a plugin that may help you out (although it is not supported for OnDemand license): https://marketplace.atlassian.com/plugins/com.pawelniewiadomski.jira.jira-openid-authentication-plugin
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