Ladybugs can be an effective way of stopping outbreaks of aphids in your garden. However, I'm not sure that you could encourage enough of them to come to your garden to control an already established outbreak. You really need to get these under control and then think about encouraging ladybugs in the future. Ladybugs need two things, insect pests to feed on and pollen. You have an abundance of aphids for them to feed on, so planting some flowers would also assist.
Eco oil is an effective way of ridding your plants of aphids. I'd encourage doing two applications.
Eco neem is also an effective product for ridding your plants of a range of sap-sucking insects, including aphids. I would suggest wiping or spraying the plant's leaves with a mild solution of water and a few drops of dish soap if you don’t have too many to deal with. Once you have wiped the aphids and possibly mites from the leaves' underside, do another application of the neem oil. - MitchellMc
I noticed ladybugs after adding a lot of flowers to garden with not much spaces, salvias might help.
A simple mix of chopped garlic in water and fresh cook oil sprayed on may help, and if your dirt is old plants would benefit by adding more new bags. - VegaNano
Here are some natural organic methods of getting rid of Aphids: http://www.naturallivingideas.com/12-organic-ways-get-rid-aphids/ - Wayne
The best natural approach is to remove them by hand. Just pop some gloves on, pull them off and drop them into a bucket of soapy water. It takes a bit of time and patience but isn't difficult. - greygardener
Just remember one dose isn't going to kill them, you need to be consistent with the spray over a number of weeks. - Matty
Be persistent with home-make organic pest control remedies. They are not poisonous and therefore you will need to apply more frequently. Also overhead watering or rain will wash off the remedy, you may need to re-apply after raining. And don't forget to apply to the back of the leaves to kill all the aphids that are hiding and their eggs. - QuailFlock