Your Oleander plant has gall bacteria.
Rough, fissured growths on twigs, branches, leaves, flowers, and seedpods, often appearing in chains. Galls start out as small bumps and grow into wart-like growths generally between 1/2 to 1 inch in diameter. Large galls may actually be several small galls that have grown together.
These galls are the result of growth of the bacteria Pseudomonas syringae inside the plant. The bacteria can enter the plant through wounds caused by pruning, frost damage or other injury or through natural openings in the leaf, blossom and stem. Water can carry the bacteria from diseased plants to healthy ones in the splash from rain or sprinklers. The bacteria is also moved from infected plants to healthy ones by unsuspecting gardeners on their pruning tools.
Prevention: Inspect oleanders carefully prior to purchase, do not buy plants that have galls.
Management: Remove the galls by pruning several inches below. Treat each cut with 10% bleach solution. Dip pruning tools in a 10% bleach solution between EACH cut to reduce the possibility of spreading the bacteria. Bag and discard cuttings. Do not compost diseased plant material.
Prune during the dry seasons to avoid infection of wounds. Avoid sprinkler irrigation while pruning wounds are fresh. Severe infection of large shrubs is difficult to control by selective pruning. Even if you cut down the entire shrub, the new succulent growth will still be extremely susceptible to infection. In certain situations, removal of the diseased plant and replanting may be the best method of control.