Hi there,

You can achieved that by going to Backend>Components>EasyBlog>ACL>Type of user group>Compose/Manage as shown http://take.ms/73bOw. You have to disable 'Moderate All Entries In Dashboard' in order to prevent them to be able to edit others user's blog. And for them to be able to create a new post, you have to enable 'Allowed To Write New Post' on "compose" tab.

Please give it a try and see how it goes