Read your story out loud.
I know the idea sounds ridiculous, but I want you to give it a try. There's no easier way to check if your writing is too stilted or formal than to read it aloud. You can absolutely do this in the privacy of your own home, but if you want an extra pair of ears to follow along, there's nothing wrong with reading it to a trusted friend, either.
If the words coming out of your mouth sound strange or make you stumble, it's a surefire sign that you need to relax and tweak your writing. Your reader will feel the awkwardness as she reads, so you want your prose to be as natural as possible. You also don't need to read the entire manuscript at once. Break it up into chunks. Maybe by paragraph or page. But definitely give it a shot. I think you'll find it incredibly helpful. Good luck!