Yes, you can delete posts and comments that you made in these areas: on the Chatter feed on your profile, on records you own, and on posts and comments you’ve made in other feeds. Deleted posts or comments will disappear and you can’t restore it (from Recycle Bin). Users with the Modify All Data permission or Moderate Chatter permission can delete all posts and comments.
Here a quick summary:
- User can delete their own post or comment
- User can delete other people post to their feed
- User cannot delete other people feed
But, if you are group owner of a group, you can do more things within the group:
- User can edit group setting
- User can edit group information
- User can edit group description
- User can delete people comment to group
- User cannot delete feed on group change
Extra: use @username to show your post on user feed, even that people is not following you, the followers of that user will see that feed as well.