If you're a fan of the offbeat, the eccentric and the unusual, you could take a few cues from the singing career of Tom Waits. He's the man with the golden gravelly voice, the veteran lounge singer, a Hollywood scavenger and a true musician. Singing like Tom Waits is more than just a vocal trick, it requires combining the vocal style with the ambiance Waits creates through his music.
Affect the unmistakable rasping sound of Tom Waits. Listening to him, you assume the man smoked three packs a day for a couple of decades. Who knows where the rasp came from? Try mimicking the sound by closing your throat a little and pushing the words through your epiglottis. If it hurts, you're doing it wrong.
Perfect the low, conspiratorial growl. In many of his songs, ("What's He Building in There" or "Cemetery Polka"), Waits growls his way through a monologue as if he's singing to someone next to him.
Try the plaintive tone Waits uses in melancholy dirges like "Cold, Cold Ground," "Waltzing Matilda," and "Innocent When You Dream," among others.
Find eerie, offsetting, authentically weird Waits-esque lyrics. Listen to songs like "Singapore" and "Jockey Full of Bourbon" for the esoteric poetry that Waits puts to good use in his own unique way. Writing your own Waits-type lyrics takes time and a boatload of creativity.
Get good accompaniment. It doesn't have to be a full band, but rather, a minimalist approach ("Clap Hands") or just piano ("Innocent When You Dream"). In these and other songs, percussion and instrumentation blend into a single stream of quirky sound. Find musicians who can keep up with composition in the spirit of the very diverse Tom Waits genre.