A wide variety of aphids, mealybugs, and scale insects suck on the sap of plants. These insects develop and reproduce rapidly. Large colonies develop on the branches and leaves of shrubs and trees. The sap goes through their bodies so fast that it can’t all be digested. Some of the sugar is still in the droppings of the insects.
The sap falling from the insects in the tree is called honeydew, and it is sometimes so prolific that it can be seen raining out of the tree. Ants, bees, wasps, and other insects can be attracted to the surfaces coated in honeydew.
The first thing you need to do is figure out which insect is growing on which plant. These insects can be treated in a variety of ways. If the plant is not producing fruit for consumption, a systemic insecticide can be used that kills the insects sucking on the plant. Soft-bodied insects such as aphids can often be treated with insecticidal soap. Hard-bodied insects such as scales have a life cycle stage that can be treated with insecticidal soap, but only at a specific time. Aphids often congregate on just a few branch tips, so pruning might reduce the population to manageable levels. Ladybugs and other biological controls are available depending on which pest insect you have.
Second, depending on how much of the tree is coated with sooty mold, you may need to wash the plant. The plant will drop any leaves that have so much sooty mold that the leaf doesn’t photosynthesize enough. It is tedious to wash each leaf, but I have done it myself on small potted citrus trees that were growing in a greenhouse. I found plain water and a washcloth worked better than paper towels.
Sooty mold will grow on any surface that is below the infested tree. Cars, patio furniture, and paving can all turn black. Soapy water works better on these surfaces. Soap on the plant leaves can wash off the protective wax on the surface of the leaf, so don’t use it.
I have seen sooty mold growing on hummingbird feeders and the surfaces under a hummingbird feeder that was dripping too much as it moved around in the wind. Hummingbird feeders with the liquid storage area at the bottom, under the feeder holes, leak less than feeders with the sugary liquid stored above the holes.