Why can't I delete messages from my IMAP account on my iPhone 4?
Maybe the trash folder is not correctly set on your iPhone.

Depending on the email-provider, you may have to choose the correct "deleted" folder in your account settings on the iPhone.

(maybe the translations are not literally, i am using a German iPhone):
Go to "Settings" -> "Mail, contacts ...", choose your IMAP account, choose "account info", look at the bottom and choose "advanced".

Here you can choose which folder is your trash folder.