GPG Invalid Signature

I am having problems with the following (in an attempt to remove hyperlinks, I have removed one of the "/" from the addresses):

W: GPG error: http://archive.ubuntu.com oneiric Release: The following signatures were   invalid: BADSIG 40976EAF437D05B5 Ubuntu Archive Automatic Signing Key <[email protected]>

W: GPG error: http://ppa.launchpad.net oneiric Release: The following signatures were invalid: BADSIG B725097B3ACC3965 Launchpad lffl

W: GPG error: http://ppa.launchpad.net oneiric Release: The following signatures were invalid: BADSIG 4874D3686E80C6B7 Launchpad PPA for Banshee Team

W: GPG error: http://archive.getdeb.net jaunty-getdeb Release: The following signatures were invalid: BADSIG A8A515F046D7E7CF GetDeb Archive Automatic Signing Key <[email protected]>

W: GPG error: http://badgerports.org lucid Release: The following signatures were invalid: BADSIG C90F9CB90E1FAD0C Jo Shields <[email protected]>

W: GPG error: http://ppa.launchpad.net oneiric Release: The following signatures were invalid: BADSIG 976B5901365C5CA1 Launchpad PPA for transmissionbt

W: Failed to fetch http://ppa.launchpad.net/dlecan/openjdk/ubuntu/dists/oneiric/main/source/Sources  404  Not Found

W: Failed to fetch http://ppa.launchpad.net/dlecan/openjdk/ubuntu/dists/oneiric/main/binary-i386/Packages  404  Not Found

W: Failed to fetch http://ppa.launchpad.net/sevenmachines/flash/ubuntu/dists/oneiric/main/binary-i386/Packages  404  Not Found

W: Failed to fetch http://ppa.launchpad.net/sun-java-community-team/sun-java6/ubuntu/dists/oneiric/main/source/Sources  404  Not Found

W: Failed to fetch http://ppa.launchpad.net/sun-java-community-team/sun-java6/ubuntu/dists/oneiric/main/binary-i386/Packages  404  Not Found

I have tried the following solutions which were in a closed case titled "The following signatures were invalid":

First of all try

sudo apt-get clean

sudo apt-get update && sudo apt-get upgrade

Some ISPs cache the packages and errors like these are reported then. 
If the above commands don't work, try

sudo apt-get update -o Acquire::http::No-Cache=True

and again

sudo apt-get update && sudo apt-get upgrade

If it still doesn't work,

sudo apt-get update -o Acquire::BrokenProxy=true 

sudo apt-get update && sudo apt-get upgrade

Try this one :

sudo apt-get clean
cd /var/lib/apt
sudo mv lists lists.old
sudo mkdir -p lists/partial
sudo apt-get clean
sudo apt-get update

You have an "interesting" set of PPAs installed:

The one's reporting BADSIG can be solved by following this Q&A:

What is the easiest way to resolve apt-get BADSIG GPG errors?

The 404 errors basically mean those PPA's no longer have oneiric repositories. You should untick those from Software Sources.

The jaunty-getdeb & badgerports.org repositories are not valid for oneiric. Again, untick those from Software Sources.