The soaps will help to control soft-bodied insects such as spidermites, thrips, mealybugs, whiteflies and aphids. Insecticidal soaps penetrate and clog their bodies membranes, thereby killing them. You can buy a commercial soap product, such as Safer's Inecticidal Soap, or make your own insecticidal soaps which can prove very effective against your garden pests. Mix three capfuls, of any of these soft soaps, with one quart of water, for a very effective insecticidal soap. These soft soaps will only last about a day before they dissipate, and need to be reapplied after above ground watering or rain.
Nicotine can be a very effective method of pest control as well.
It is naturally derived, however, it is not usually used in organic gardens due to its toxicity. Nicotine can be deadly to most insects and humans, when swallowed in concentrate. This poisonous compound, affects the neuromuscular system causing insects to go into convulsions and die. Sometimes you can see it sold commercially, mixed with sulfur. One commonly used product is Black Flag's Nicotine Sulfate.