I know that I'm not the greatest singer in the world but I'm able to hold a note and keep in key. The problem I find is that years of singing other people's songs has meant that I tend to emulate the original singer and it becomes more karaoke. I do a brilliant Dave Mustaine!

This was never an issue as really I was a guitarist who occasionally did backing vocals. I have, however, always wrote songs and I now have enough material to record an album. These songs are very personal to me and I feel they work best acoustically, ie. just me and a guitar.

The problem I'm finding is I don't really know what my natural singing voice is and I end up either doing rock clichés or impressions when I want a more folky/singer songwriter vibe. I also am not really sure what my natural range is. I can hit higher notes in a Jack Black style but it is very forced and unnatural.

My key of choice is generally Ab minor (capo on 4th) which really fits my voice (or at least the one I tend to use) but I want to break out of that as it means my songs all start to sound the same.

Any advice on the things I've mentioned (or in general) would be much appreciated
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As for your range - If when you sing very high notes you feel easy and can imitate an Opera singer, that's called "falsetto" and that's not your natural range. If you feel like you're speaking, you're still in your natural range.
As for the natural voice - try just to speak the lyrics and slowly add the melody, and if you can, make the two phases sound as similar (tonally) as possible.
Spend a few sessions with a vocal coach who has cred. A second set of trained ears guiding you through vocal passages is hard to beat.
"Your sound is in your hands as much as anything. It's the way you pick, and the way you hold the guitar, more than it is the amp or the guitar you use." -- Stevie Ray Vaughan

"Anybody can play. The note is only 20 percent. The attitude of the motherfucker who plays it is 80 percent." -- Miles Davis

Guthrie on tone: https://www.youtube.com/watch?v=zmohdG9lLqY
That took me a while. There are some good YouTube videos you could checkout. Eric Arcenaux is one guy that I thought had some helpful videos.

If you learn proper technique, about head voice and chest voice, (chest voice is what earlier commenter mentioned was natural range, and head voice is higher up, but is not falsetto, it is different, but in similar range to falsetto.), then you'll understand how your technique should feel, you'll get diaphragm singing, you'll feel free and clear in the neck and upper throat, and your natural voice will make an appearance.

You might find it doesn't match music you already wrote at first. Or not the way you would have liked originally. It took me a little while to really get what I was supposed to be doing, and then recognize what my voice was, and then develop that into my style.