Okay, your question was kind of muddled, so I'm going to make some assumptions here.
1. You are unable to play music on your iPod, which you just stated you didn't have, so I'm going to assume the second "iPod" was used generically for "non-iPod mp3 player".
2. I'm going to assume by .mp4e you mean "songs I downloaded in iTunes", since I've never heard of .mp4e, .mp4 is generally a video file, and iTunes generally uses .m4p files.
Right. Now that that's out of the way, let's get down to brass tacks.This is why you shouldn't buy music from iTunes!
Seriously. If at all possible, get MP3s from some other legal source like Amazon. Then you can do what you want with the files you bought.
The problem here is that Apple has actually been pretty successful with their DRM (Digital Rights Management) that restricts usage of that file. I'm kind of surprised it hasn't been hacked, actually, but there still isn't a good direct way (that I know of) to convert from m4p to mp3. However, it can be done and there are two main lines of attack.
The tried and true method is to burn your songs to a CD, which iTunes allows and which turns them into the unprotected CD format, then turn around and rip them back into MP3 format. Unfortunately, this gets very tedious for large amounts of files and wastes lots of CDs. That's why clever people thought to use a CD-burner emulator. This tricks iTunes into thinking it's burning to a CD, but really it's writing the CD format to your hard drive. From there, you can emulate an MP3 rip without actually using a CD. Some programs that do this are NoteBurner
and CD Emulator
, and one for Mac here
The other main line of attack is to let iTunes play the song, then record the audio feed and encode it to MP3. You can find a big list of programs that do this here
Many of these programs will cost you some money, but that's what you get for shackling yourself to Apple. And of course, it's probably technically illegal, so you've got that to worry about as well. Good luck!