How can i delete threads on my profile

You can't delete your own threads. I believe Moderators have that ability so you could try PMing  one of them. 

We can't edit or delete threads from the profile, either.  We can delete a thread from the forum, but this is not something that is done just on request, because it is old or completed, etc.  We do it because there is some reason that it is better for BYC that it be removed.

Why do you want to "get rid" of them? 

Is it an issue of being subscribed to them?  If you're not subscribed to them, you may never even come across them again, which is kinda like getting rid of them.   You can go into your subscriptions and edit the settings in pretty fine detail.

When you say you "couldn't" unsubsribe, please provide more details that will help us find, duplicate, and hopefully resolve the problem:

•  Did you receive any error messages?  if yes, what were they (please copy and paste the entire message, screenshots are best)?
•  What were the exact steps you took before having the problem?  Please be as specific as possible so we can do exactly what you did.
•  Which browser and version are you using (eg., Firefox 3.5.9, Internet Explorer 7, etc.)
•  Have you logged out, deleted your internet cache, logged back in, and tried again?
•  Have you tried a different browser?
 

Once you unsubscribe from an item you should definitely not receive emails any more.   Unsubscribing is a pretty easy process: http://www.backyardchickens.com/a/subscription-tutorial (specifically the "Edit Your Subscriptions" section)