From the pictures, it appears you have to different types of algae. The greenish stringy kind is hair algae. The black tufts on your java fern are black beard algae. Green hair is easy to remove, I use a toothbrush like a comb and pull it away the plants and moss. This will always take some moss away, but it will grow back. Green hair algae can be caused by too much light. The nano light is fairly strong, what size aquarium is it on?