Birds of course the right species enjoy eating aphids as do yellow jackets and several species of bees and lots of other 'pests'. Try these: Black Aphids are tasty too: http://www.small-farm-permaculture-and-sustainable-living.com/natural_pest_control_aphids.html As aphids are near the bottom of the food chain an infestation serious enough to do major damage or kill a plant is a indicator of the unnatural absence of other predators. Of course if you are surrounded by commercial crop lands then the environment you live in is likely to be largely unnaturally devoid of aphid predators. It's the presence of predators that keep aphid and spider mite as another example populations under control for example on a patio plant you keep out side in the summer but come winter, when you bring the patio plant indoors those patio plants often succumb to aphid and spider mites infestations away from their predators during the winter. Here is a link that might be useful: Aphid Control Chickadee example

Try adding some Lacewing Larvae loose on your plants. They can be purchased online. They'll stick around until they mature into gossamer winged insects. If you've used Safer Soap or Neem, make sure you wash it off and let leaves dry thoroughly before applying. I always grow milkweed in the garden for two reasons: 1 They attract and support Monarch Butterflies. 2 They get a special orange aphid that attacks nothing else, except Oleander. The infestations can be severe, but the MW seems to tolerate it. This serves as a beacon and way station for beneficials who clean up the milkweeds and disseminate into the garden, mopping up as they go.

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I don't know from picture what they are, but I'd use Spinosad. Just spray before the bees and butterflies wake up. It is organic.