I agree with Articuno that mealies are much harder to get rid of, and that they are world-class hiders, often running hidden mealie-factories where you'd never guess. They are really devils disguised as white fluff.
Aphids give birth to *pregnant* young, so they don't have to hide anywhere to take over the universe. They just have to be there. They tend to cluster on tender new growth and buds, so you don't have to search for them. They're brazen, just sit there and chomp away.
Knowing these two things tells you how to get rid of them--
1. you have to spray or wash them off every 3-5 days. They will keep coming back, and remember just one = thousands because of the pregnant young thing. So you need a persistent campaign against them for a couple of weeks. Spray them off. Three days laters, repeat. Repeat, repeat. Each time there will be fewer and finally in a couple of weeks there's a time when you don't see any.
2. Brookn's recipe, insecticidal soaps all work. So does plain soapy water-- the soap dissolves the exoskeleton and they just slide right off and drown. Even just a high pressure stream of plain water from a hose will do it. I usually use soapy water sprayed on with one hand and slide them off the plant with my other hand.
It's not what you spray on them that ends the infestation, it's the *persistence* you use in keeping after them.
3. If you suspect there are insect eggs or other nasties in your pots, you can use Safer's Insecticidal (Insect-Killing) Soap as a drench quite safely. /the killing is actually mostly done by the Soap, believe it or not. Because of the soap, it does have a detergent effect on the medium, making it super wet to be careful with the watering for a week or so after drenching.
PS Scale or mealies on oncidium spikes are very hard to get rid of without destroying the spikes.