Question
About a month ago I noticed these worms on my Oleander bush. I took them off and put them in soapy water.  I thought that was the end of them.  Wrong.  I notice some brown leaves today and then noticed the worms were back again.  They have a yellow body with black feelers on them.  So the question is how can I permanently get rid of them.

Thank you for your help,

Marion

Answer
The Oleander caterpillar is the most significant insect pest of oleanders. The caterpillar is an immature (larval) phase of the Oleander Moth, Syntomeida epilais jucundissima. The adult female moth lays clusters of 25 to 75 orange eggs under leaves. Young larva will skeletonize the leaves, while the more mature, orange-colored caterpillar with black spots and hairs will eat the entire blade. By biting the veins, the caterpillar drains the toxic sap before consuming the leaf.

When it reaches a mature size of about 2 inches long, the insect pupates. The silk-covered cocoon yields a purple-black winged moth that has several white dots on the wings. With a sixty-day life cycle, this pest can have three generations in a year. Scouting for the eggs and young caterpillars in March, July and December will enable control measures to reduce feeding damage. Bacillus thuringensis insecticides can provide environmentally safe yet effective control. Chemical insecticides also can be used.
The adults do not look like "normal" moths or butterflies.  The adult stage of the oleander caterpillar is sometimes called the "polka-dot wasp moth." Wasp moth is the common name given to the subfamily of arctiid moths to which this species belongs (the ctenuchines) because of their resemblance to wasps such as the sphecids and pompilids.  

The oleander caterpillar is a native of the Caribbean region. Its range extends from northern South America, through Central America into Mexico, and from many Caribbean islands into Florida and coastal regions of southeastern states. It is a year round inhabitant of south Florida and the Keys but is usually killed by cold winter temperatures in northern and north-central Florida only to recolonize these areas the following spring. The original host plant is thought to be a now relatively rare beach- or pineland-inhabiting vine, Echites umbellata Jacq. However, the oleander caterpillar is thought to have switched over to feeding on oleander when the Spanish introduced this Mediterranean ornamental plant in the 17th century. The geographic distribution of the oleander caterpillar in America now coincides with that of oleander except that the caterpillar is not found in California.

Birds do not eat oleander caterpillars because they are full of toxins from oleander plants. Stink bugs, parasitic tachinid flies and wasps, red fire ants and spined soldier bugs all eat oleander caterpillars. These beneficial insects often do not exist in large enough numbers to prevent damage to oleander shrubs in summer. Caterpillars may be picked off and destroyed or drowned in soapy water. The hairs on the oleander caterpillar do not sting. Gardeners can spray plants with the microbial bacterium Bacillus thuringiensis, known as Bt, which is ingested by the caterpillars as they eat leaves. Repeated applications are needed after heavy rains.

Read more: Oleander Caterpillars on Plants | eHow.com http://www.ehow.com/info_8274546_oleander-caterpillars-plants.html#ixzz1YE1CQ03A

Here is a web site that gives you more information on the moth.
http://edis.ifas.ufl.edu/pdffiles/IN/IN13500.pdf