Getting rid of aphids
It is possible to get rid of aphids with sprays or ladybugs, but the sprays only work till the next rain and the ladybugs will end up in the garden which has the most aphids which is probably your neighbors.
An answer for people who like to fuss
Here is a natural insect spray: Blend together 1 garlic bulb, 1 small onion, 1 t cayenne pepper, 1 quart water. Steep one hour and add 1 T liquid hand soap. Store in the refrigerator.
This is a permanent solution.
Plant allium (chives, garlic, onions) as companion plants surrounding or bordering the plants which are susceptible to aphids. The allium has to be in the ground year round. This method has kept my garden aphid-free for 15 years, even though it is neighbored by aphid-laden trees.