These odd growths have recently appeared on my umbrella plant. Does anyone know what they are?
They are aerial roots; whilst Schefflera is capable of producing these, it doesn't usually unless it's stressed. They are often produced when Schefflera is trained as a bonsai, where its growth and roots are very constricted. I can't see how tall your plant is, nor can I see the base of that stem that's dropped down and forwards - is it healthy or partially damaged? It's likely that your plant needs a new, bigger pot and some fresh potting soil, especially if its quite tall. If you don't like the aerial roots, cut off the stem which is producing them and improve the plant's overall health, correcting its growing conditions by repotting.
If it was severely neglected and its not a good shape or looking poorly lower down, and it is tall, you can create a new plant for yourself very easily. You just need to cut off about 6/8 inches from the top of the plant, cutting just above a leaf, then strip off the lower leaves on the cuttings, leaving 2 or 3 at the top and pop them in a bottle of water. Leave on a windowsill, keep the water topped up and when they form roots (usually around 6 weeks) you can pot them up, carefully so as not to damage the new roots.