If you posted the entry yourself, you can both edit and delete it, as long as you are still a member of the asylum. If you are the community's maintainer, you can delete the entry, but you can't edit it in other ways.
While editing entries, if you receive an error message that states "Client error: Invalid text encoding: Cannot display non-Unicode posts unless default encoding has been selected", see https://www.insanejournal.com/support/faqbrowse.bml?faqid=21 . This process will need to be done by the community maintainer.
If you are the maintainer of the asylum, but are getting errors when trying to delete the entry, make sure you are logged in to the maintainer account.
USING A DOWNLOADED CLIENT:
Many clients available for download include the ability to edit or delete entries in an asylum. For more information on your preferred client, consult its documentation or its menu options.