Check you've got "bulk edit" in the global permissions and check you have "delete issue" permission in the project(s) you want to delete them from.
Run a filter that finds them, and use bulk edit -> delete
Note that a standard recommendation is to not allow delete issue most of the time because it's very hard to recover a deleted issue - use it temporarily to do this!
Ah, sorry, I misunderstood. There's no easy way to remove large numbers of issue types. You'll need to go to Admin -> Issues -> Issue types and manually remove each one. If JIRA is currently using it (i.e. you have one or more issues of that type) it will ask you what you want to convert them to. If you're going to get a lot of those, then I'd suggest doing a bulk edit so you don't have to do that migration on every delete.
It's been quite a while so I'm sure you have solved this problem. However for others who might have come across this page looking to solve a similar issue, I would recommend an app called Cleaner for Jira. It works for both Jira Cloud and Server.
The Server version of the app displays a vast number of configuration items (Projects, Custom Fields, Issue Types, Workflows etc.) as well as their usages and you are able to delete them from the page itself.
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