Evernote is absolutely perfect for songwriting. I use it each and every time that I write a song.
Lyrics: just type out the text
Melody, harmony, rhythm etc: just make an audio recording note
Guitar chord shapes: I have an iOS app called reverse chord finder. (https://itunes.apple.com/us/app/reverse-chord-finder-pro-inverse/id379856345?mt=8) It's only $10 but there's a free lite version as well. This app lets you "type" in chord shapes on piano, guitar, ukulele, bass etc. Just press the keys/frets and it'll tell you the name of the chord. No music theory necessary (though music theory is always helpful. ) Sometimes I have a very specific chord that I want to play with a very odd inversion or fingering. So what I do is I type out the chord that I want then I take an iOS screenshot (simply hold down the lock button and then press the home button). Then I go to evernote and add a picture. I choose the screenshot that i just took.
Now within the span of a few minutes I have lyrics, melody, harmony, rhythm, and even chord voicings all in one easy to find place. This way of songwriting is especially helpful because the moment of inspiration can leave you in the blink of an eye. Before evernote I was lucky if I wrote a new song every few months. But now I have times where I have a new idea sometimes every day for weeks. I am literally writing songs faster than I kno what to do with them!
I love evernote.