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This is sooty mold. It is a byproduct of a pest infestation, likely aphids or scale. This article will help you with getting rid of it: https://www.gardeningknowhow.com/ornamental/flowers/camellia/sooty-mold-on-camellia.htm

You don't say if you want to transplant the camellia, or simply get rid of it. If you want to move it, this article has a lot of good information: http://www.aces.edu/counties/StClair/documents/NRCamelliaMoveGlover09.pdf
If you want to totally get rid of it, consider that many people love camellias. You could contact some nearby nurseries or landscapers, or run an ad, to see if anyone would like to have it. You could probably even offer it for sale. This way, you don't even have to go to the work to dig up the plant, and someone else still gets to enjoy it.

This is called sooty mold, which more often than not is brought about by some type of pest, like aphid or mealybug. I would recommend neem oil. We have found it to be very effective against these kinds of pests and will also help treat the sooty mold. These articles will explain more: https://www.gardeningknowhow.com/problems/pests/neem-oil-uses.htm, https://www.gardeningknowhow.com/ornamental/flowers/camellia/sooty-mold-on-camellia.htm

It could be suffering from over watering or it could have a fungus (brought on by the excess moisture). There is not much you can do if the issue is overwatering as it was brought on by heavy rainfall and the soil not being able to take the water away quick enough. But, if the rain stops and the water drains from the soil quickly, the plant should recover. As a precaution, I would also recommend treating for a fungus. This can cause these symptoms as well. A general fungicide would be all you would need to do this.

This article contains information that should help you: https://www.gardeningknowhow.com/ornamental/flowers/camellia/pruning-camellias-how-to-prune-a-camellia-plant.htm