Is there a formula books use to set the moneyline?

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Say the spread is X and I bet the moneyline, is there a formula they use to set the payouts?

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Basically, yes. The "formula" depends on the sport. Given enough historical data it's pretty easy to calculate for yourself.

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Or if I adjust the spread by Y, how does that affect the payouts?

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Do you mean, do books automatically adjust the ML as they adjust the spread and vice versa? The answer is that they often do, but not always.

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Do the books often fudge these numbers based on action? (they seem to not be totally concistent all the time).

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Sometimes they do. A good example is last year's Superbowl. The ML and spread numbers were significantly out-of-whack compared to each other. If you go back far enough, you might find a thread or two on this forum discussing this specific issue.

To answer your unasked question, sometimes one or the other is a better value, and if you know how these numbers ought to relate, you can often determine which of the two is the better bet.