I don't know where it originated, but it sounds like an americanism to me. As far as I know, it means much the same as "every which way", which also sounds as if it travelled eastwards over the Atlantic!
For example, someone might well say, "I've tried to solve this six ways from Sunday", meaning he has tackled the problem in every way he can think of and none of the approaches has worked.
I've never heard this expression before (nice one, I like it) but the first thing that springs to my mind is that it may have at one time referred to the six days of the week barring Sunday, when you "should" rest.
To my ears it also has a fairy tale ring to it - I envision the hero of the story setting out to solve a problem / slay the dragon / rescue the princess, and trying a new way with every new sunrise. But this is just my imagination!