Why isn't there a delete button in my own polls and clubs?

Once a club has been created, it doesn't just belong to whoever created it. It also belongs to other members, and to Fanpop in general. That's why a club can't be deleted. Even if you've lost interest in it, there might be others here who like the topic and might want to join.

I think it might be possible to leave a club once you're not the only member, so if others have already joined this might be your best bet. Otherwise, you can report the club if it's a duplicate or inappropriate, and get it deleted that way. You can't report it for deletion just because you now think it's a stupid topic for a club, though.

Polls are the same way, belonging to all of Fanpop and not just you. I think it's possible to edit/delete polls for a few minutes after creation, but not later. Otherwise people would just spitefully delete any poll whose results weren't going the way they wanted.