It sure sounds to me as if your Oleander (Nerium oleander) has Mealy bugs, and they can damage your plant if left unchecked. There are many species of this insect and I don't know which you have, but here's what I would do. Since the Oleander is a sturdy plant, set your hose nozzle to a sharp stream setting and dislodge the critters. If that doesn't send them elsewhere, then try the dishwashing liquid detergent method. Add a tablespoon with a cup of water to your hand-held sprayer and spray your bush making sure to get the undersides of the leaves. Take care to treat only your Oleander as even dishwashing detergent can harm tender moth and butterfly caterpillars.
Enjoy your Oleander now, but in the back of your mind be thinking of a replacement since these plants are being eradicated in Texas by a deadly bacterium. Spread by the Glassy-wing Sharpshooter, this disease has all but eliminated the Oleanders in Galveston (the "Oleander City") and it is moving northward. At this time there is no known treatment for Oleander Leaf Scorch, appropriately named for the appearance of an infested plant. A good replacement would be an Evergreen Sumac, an equally large evergreen shrub with shiny dark green leaves. Its furry red berries offer special wildlife treats in the fall.