This took much searching I knew it had to be possible but finding information on how to do this took some time. I finally found a post on a Google help forum with someone who did a blog post about it. Tweak My Blogger has an excellent how to on how to do this by hiding it with CSS coding. I am going to show you how to hard encode it using HTML this will be more permanent if Blogger decides to reset anything.
TO REMOVE POST ATOM LINK:
Log into Dashboard –> Design –> Edit HTML –> Expand Widgets –> BACK UP YOUR TEMPLATE (DOWNLOAD YOUR HTML CODE!!!) Trust me this will save you a ton of headache.
You will need to find this code: ]]></b:skin>
The easiest way to do this is on a PC Control F or on a MAC Command F for the Search Box to open. Insert that code in the search box –> Search
TO REMOVE HOME AND OLDER POST LINK:
Insert the following code BEFORE ]]></b:skin>