What software do I need to edit commercials out of recorded sports games?
Allow me to edit out commercials anywhere in the video.


Any modern editor can do this (Adobe Premier, Sony Vegas, Final Cut etc) including light-weight (ex. Pinnacle Studio) and free editors.


  After editing, it keeps the 5.1 Surround Sound.


Provided your original clip contains 5.1 channels and your editing environment is set up with (and can support, see more professional packages) 5.1 support, and you export in a format that support 5.1, this is granted.


  Burn the video to a Blu-Ray player or save it to disk.


As long as you export in a format supported by the BD-disk creator software, or a format that can be trans-coded, no problem.


  Ability to add menus too my Blu-Rays.


This most BD-disk creator software can do (see for example Adobe Encore).


  If there are logos on the screen(say ESPN logo), be able tell the software to find all instances and remove it.


This is a very specific task and as you say, you need to tell the software to find these. You can do this by combining a tracker to the logo and a script that can follow. When logo is "lost" for the tracker, init a method in the script that do what you want. This as said, will be very specific and it will require you to program your script very specific.

IMO it will be quicker to go through these manually. especially if you know the material you're working with or at least what to expect of it.