The simplest, quickest, easiest way to get rid of Aphids is a sharp stream of water to knock the wee buggers off the plant. A hand held spray bottle does work really well for this because your garden hose pressure could wreak havoc to the plant. If an Insectidical Soap is desired, and it is not really as effective as simply knocking the buggers off the plant, you need a real soap and none of the "dish soaps" are soaps. The "dish soaps" are detergents which can cause serious harm to plants. Murphy's Oil Soap is a real soap and can be used just as an of the other real soaps. Mix 1 teaspoon of that soap in 1 quart of water. More often than not when spraying the IS on Aphids you knock the wee buggers off the plant anyway so adding the soap to the water is not all that more effective. Spaying with the IS after you clean that generation of Aphids off the plant may help control the future generations that will be moving in. The best, most effective means of control of Aphids is to be sure the soil your plants are growing in is a good, healthy soil that will grow strong and healthy plants that will be less attractive to insect pests such as Aphids.

Insecticidal soap and Neem oil only work on contact. They will kill any soft bodied insect. Ants are not considered a soft bodied insect and that's why it does not work on them. From the document linked below: What is Insecticidal Soap? All soaps are made of salts and fatty acids, but not all soaps are good for killing insects. Some soaps can be highly destructive to plants and are useful as herbicides. Insecticidal soaps, however, are specifically formulated to kill insect pests while having few adverse effects to people, plants and the environment. Insects must come in contact with the soap before it dries in order to be controlled. Therefore, thorough coverage to both tops and bottoms of leaves is essential. Do not apply insecticidal soaps directly to water or use near a water source. Multiple applications are needed to control most insects. Hard water is not effective for mixing soap sprays, so use softened or distilled water for best results. Read on for more info like this. Here is a link that might be useful: Insecticidal Soap

Its perfectly safe. Neither does it harm blossoms or growing fruit. Just follow the directions, and don't spray when the plant is in direct sun or its over 90F. In evening is perfect.

Get one of the inexpensive hand pump or compression sprayers. These are what I use and they are work perfectly and are easy to use. And regardless of whether you are practicing organic methods or not, it is advised to have a sprayer dedicated to a specific purpose - insecticides in one, fungicides or fertilizers in separate sprayers, and if you use them at all, herbicides MUST have their own.