OMF=Open Media Framework. It's a platform-independent file format for transferring digital media between different software applications. It is used by programs like Avid, Final Cut Pro or Pro Tools.
If you are going to have audio work done, generally you'd export an OMF out of FCP to give to your audio mixer, along with a QT of the video for reference. The OMF file contains all the media in your audio tracks, plus any handles you give it, so the audio mixer has the highest quality, most flexible files to work with. He'd then give you back an AIFF file (usually...) to match back up to your timeline for the finished audio.
EDL=Edit Decision List. It's an electronic text file of all of the events in your timeline (barring some things, but I won't go into detail...)
EDLs originated back in the way-back days of linear editing when you did one thing at a time and in order. An EDL is basically a list of the reel name, source in, source out, master in, master out, tracks used, etc. Some can track certain kinds of effects and speed changes.
XML is poised to replace EDL in many instances. More data.
Hope this helps clear some things up!
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