Hello Siby,

funny, I was also looking for the real lyrics of the song in the movie Elmer Gantry, and found your question. I thought "right, i won't find it on the web".
But I did !

The script of the movie is available, and the song has been transcribed. You can find it at that url :
http://www.script-o-rama.com/movie_scripts/e/elmer-gantry-script-transcript-lancaster.html

And the lyrics :

(choir singing "I'm On My Way")


? I'm on my way
? Off to Canaan land
? I'm on my way
? Off to Canaan land
? I'm on my way
? Glory, hallelujah
? I'm on my way
? Well, I'm on my way
? Off to Canaan land
? I'm on my way
? Off to Canaan land
? I'm on my way
? Off to Canaan land
? I'm on my way
? Glory, hallelujah
? I'm on my way
? Had a mighty hard time
? But I'm on my way
? Had a mighty hard time
? But I'm on my way
? It's a mighty hard climb
? But I'm on my way
? On my way
? Glory, hallelujah
? I'm on my way
? All along the way
? Satan lies a-waitin'
? Every night and day
? Satan lies a-waitin'
? Hear me shout and say
? Get behind me, Satan
? I'm on my way
? Glory, hallelujah
? I'm on my way
? Fight the devil and pray
? Take another step higher
? Fight the devil and pray
? Lord, I want to climb higher
? Chase the devil away
? Lord, I'm caught in his fire
? I'm on my way   
? Glory, hallelujah
? I'm on my way
? Lord, I'm on my way
? Lord, I'm on my way
? Lord, Lord
? Lord, I'm on my way
? I'm on my way