You are right. You do not have a strong voice. But you can change that. What you do have is character, and you are in tune for the most part. That you can't change.
Just keep at it. You are not a bad singer by any means. You just suffer from two very key things that most inexperienced singers suffer from. Lack of confidence and lack of experience. I know it's hard to listen to yourself sing. Trust me, I've been there. I'm still there. For as good a singer as people tell me I am (and trust me, I don't agree with them), I still get highly self conscious when I hear my recorded voice, especially in front of other people. You just have to truck on, and accept the fact that you will always feel slightly off-put by the sound of your voice. Eventually, you'll dig this guy out and listen to it, and be amazed at how much you've improved.
In the mean time though, you're voice is definitely reminiscent of Johnny Cash here. Maybe it's just the song choice, but I hear a lot of the same timbre in your voice as Johnny Cash's.
edit: I was reading through the singers and vocalists forum, and I saw this post by Swiss Army Knife, and I thought I might copy pasta it over here. It made me feel better about myself when I read it at least:
I'm a Christian rock musician. I write lots of songs, I play guitar, I play keys and I play bass. But vocals are sort of along for the ride.
For a long time, I hated my voice. And I still have my days. It's tonal quality is OK-but-not-great, but it's on pitch. Interestingly enough, I've got tons of confidence singing live, but the studio scares the crap out of me. My biggest problem is that when I record a song, I end up wishing it could sound like somebody else when I listen back.
But two people told me things that changed my life.
1. During sound checks before getting ready to sing one night, I was feeling pretty miserable about how my voice sounded. The sound guy, who is also a college vocal instructor and practically an opera-quality baritone, was having none of it.
He pulled me aside and said, "Let me tell you something. You do not have a 'great' voice. It's not opera-quality. But you need to understand something ... that is a compliment. Your voice is on pitch, it's honest as hell, and it's got BUCKETS of passion. That's what people want to hear. They can connect with you. Heck, they want to sing with you. They just get tired of me."