If you search web enough you can find JIRA’s own internalization files mainly “JiraWebActionSupport.properties” file and its locale specific versions like “JIRAWebActionSupport_de_DE.properties” etc. Since most of your user interface is JIRA specific you can reuse many translations from these files.
Use Google Translate, Yandex Translate, Bing Translate. Cross check translations from these services, given output of one as an input to another one. If reverse translation matches the original input it is a good indication of correct translation.
Use Google Images. Enter translated result to Google’s image search. If returned images matches what you are looking for it is also an indication of good translation.