When I wanted to post an audio bit on to Blogger, I was going around in circles. A whole day of search later I found the following website that can help you do it.
You need to register on this site. Go to 'Audio' and upload your audio file there. A code will be generated, which all you need to do is copy and paste on to Blogger in 'Edit Html' mode. That's it! (Hey, this code is somewhere down on the right hand panel, you need to scroll down a bit.)
NOTE: Remember that the above website only allows MP3 uploads. So what if you want to convert any other extension to MP3 and do it quick? Go to http://makeownringtone.com/. This is a free service that allows you to edit your audio bit and even enhance it. And then you can save it as any extension you want. Brilliant, really.