I am wondering is there any tool which can help visualize relations between tasks/bugs, I mean dependencies like related to/blocks/clone/etc.
There is the Links Hierarchy plugin, though I'm not sure if that supports JIRA 4.4. There is also the REST example at https://developer.atlassian.com/display/JIRADEV/JIRA+REST+API+Version+2+Tutorial#JIRARESTAPIVersion2Tutorial-Example%231%3AGraphingImageLinks
Vivid Trace visualizes relations between tasks/bugs for any/all of the issue link types you mention, and it can graph a given issue, component, version, or even a whole project. https://vivid-inc.net/
(Disclaimer: We make it.)
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