As far as I am aware, すぐに means "immediately", but in which contexts can you use もうすぐ and すぐ？
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As an example, if I'm told this I might expect the fireworks to start...
i.e. もうすぐ isn't immediately, more like "very soon". As for すぐ vs すぐに I don't think there is a difference.
EDIT: The actual time these word indicate depends heavily on the context and listener. The times above came completely from my bottom.
For example if I'm told this, I might expect my scores to go up...:
But somebody else may have a completely different expectation.