Ladybugs, Lady Beetles, are a natural part of the environment so why someone would think introducing them to your garden would be bad indicates someone that does not know much about the environment you live in. The link below, while specifically about greenhouses, has some good information about Aphids. This link, http://www.attra.org/attra-pub/gh-whitefly.html
is about Whitefly.

Here is a link that might be useful: Aphid control

Christian, purchasing and releasing ladybugs to your little patio garden will probably be ineffective, unless your patio is enclosed. Ladybugs tend to flee at the moment of release.

Also, sadly, many companies are selling non-native (Asian) ladybugs, which have dramatically overtaken the native species in the past several years. They are, apparently, easier to mass produce. There have been LOTS of discussions and research about this problem and you are correct to be concerned. Native ladybugs are harvested from the wild, and that causes concerns, too.

Attached is a good attachment about IPM practices for strawberries. Click on the links for both aphids and whitefly and spend some time reading about the cultural controls as well as organic applications.

Here is a link that might be useful: Click here

Many sellers of Lady Beetles wild harvest them, they are not grown by the sellers. Purchased Lady Beetles might fly away on release if the habitat they are released in does not provide what they need to survive, food, water, and shelter, and that is probably the major reason people see those wee critters leave, an improper habitat.
The best way to attract insect predators is to create a habitat that they like and can live in even if the insects they prey on are not around.

Here is a link that might be useful: Lady Beetles

I use a neem oil spray on my plants. Whenever I've had a bad infestation, I've used Safers Soap spray. I had a pretty bad aphid problem my first year gardening in my strawberry patch--but the next year someone recommended neem oil which worked well to control the problem. This year I haven't had any aphid problems yet. Instead, I've been dealing with an absurd amount of sparrows.

You need to release Ladybugs correctly. Wait until the middle of the night, or as late as you can stay up, and be sure to mist all of your plants with a spray bottle of plain water.

Also, it makes a big difference if you allow the aphid population to rise a little, if you have been poisoning them. The ladybugs will not fly away if they have food and are not threatened. It is important to stay out of your garden as much as possible the day after release, this is when they are most finicky and you do not want to scare them into flying.

Also, keep in mind that a normal small garden might only have a handful of ladybugs living in it naturally. If you release 3000 ladybugs, most of them will fly away, but a handful will stay and breed and that is how you get a steady population in your garden.

All of that is excellent advice, Phildeez. Thanks for the input.

It also helps to mist the ladybugs with a sugar solution something like you would make for a hummingbird feeder. This sticks their wings together for a short while so they can get familiar with their new surroundings and pack in a few calories before being able to fly.