I am new to caring for orchids. I have had these crawling around for a few weeks. I have treated with Neem Oil, but they will not go away. No webbing or other damage seems to be occurring. They are fast moving and mostly active at night. Would greatly appreciate any help identifying these crawlers.
They're certainly not the spider mites I get. They're red to reddish brown and rather slow moving.
If you have spider mites, you will soon notice white pitted areas on both sides of the leaves. I am not sure what these are. Aphids may be a good guess.
I agree on the aphis diagnosis. There may be something else in your growing area that is attracting them. Pick up a yellow "sticky trap" and hang in the area to dispense them if you want to go "green". There are also chemical sprays if you prefer but generally a thorough washing of all the plants in the area several times is enough to get rid of them or at least discourage them dramatically.
For any pest the best cure I have found is a bucket full of tepid water with a dose of thick bleach. Just soak the whole plant for a minute or so and the bugs will have been eradicated. I have known it to get rid of fungus as well. Give it a try it wont hurt the plants.