I agree you may have a bent strut, it can cause the symptoms you describe. The oscillation in the shaft though is more indicative of a bent shaft. Once you correct all that you'll need to realign the engine anyway.
Running aground will do all of it, as well as the props.
I'd compare the strut with the one on the other side and/or check it with a square. If it's seriously bent you should be able to see any difference. If it's only minor, realigning the engine may be all you need to do. Uncouple the shaft from the engine and slide it back half an inch, any misalignment will be apparent. Then spin the shaft by hand. if it still wobbles it's bent.
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