"How can I download all the iTunes songs I have purchased since 2008? "
Do I need to de-authorize my previous computers and authorize the new iMac?"
You will need to authorize the new computer.
Go to the iTunes Store, log into your account, and click the Purchases link under the Quick Links. From there you should be able to re-download some or all of your purchased content. Note that not all content has been licensed for re-downloading in all countries at this time. You can see what content you can download here:
For full instructions, see: