The response at a local newsgroup regarding white flies and moths in a greenhouse:

I don't use any chemicals. A good way to get rid of these pests is to get some yellow poster board.  Spray it with adhesive.  These bugs love the color yellow!
Also spray your plants with water every day in the evening.  Those two combinations should do the trick!

I didn't know that they like YELLOW, but have tried “sticky traps”  before and of course the fly strips.  They definitely work, but I got the store-bought stuff.  Don't know what adhesives to spray.  Dipping it in honey comes to mind.
I controlled APHIDS outdoors on the oleander at my old place mostly by using the garden hose sprayer set to high pressure.  I only planted the oleander because I thought it wouldn't be eaten,  but I lost entire bushes to gophers/moles and the aphids loved it.
The last couple days I've done major “spring” cleaning in the greenhouse as we took many seedlings outside and I cleared off all the shelves.
I took out the black plastic strips we set the trays on and had in the window for shade and heat gain and replaced it with white plastic.  It's warm enough now. 🙂
Also sprayed diatomaceous earth, especially under the plastic strips covering the wood shelves.  It's worked GREAT in the year we've been using it.  The ants come in, we spray, they're gone.   It also greatly reduces the occasional gnat infestation and we have no spiders.  I hate spiders.
I don't like to use D.E. outside because it kills ALL insects including the beneficial insects.
And we have to be careful to not get D.E. in the worm bin.
For mites we spray some organic soap water.
It works every time and immediately.  I find it's a good idea in a densely populated greenhouse with lots of basil and tomatoes to spray once a week or so.   An ounce of prevention …
CRICKETS
The D.E. did NOT work for crickets last year, although maybe we just didn't wait long enough.   Since we had just completed the building, it was infested with crickets and I finally took the plants out and set off a bug bomb.
Now the crickets are out in full force again and last night I captured one in the the greenhouse.  Strangely, it didn't jump as I expected when I tried to coax it into a cup.  It just kept running away, and eventually I caught it and threw it out.
We sure hope we don't have another cricket invasion.
GRASSHOPPERS
We saw one in our raised bed the other day and it sure had done some damage.   The bed is covered with 1/2″ hardware cloth and obviously that's too big.  We're about to tack some shade cloth over it.
Last night I also saw a gazillion moths OUTSIDE the greenhouse, attracted by the light.   Not a problem, as long as they don't come in.
I'm sure we'll get our share of horn worms on the tomatoes, eggplants and squash again, but last year we just picked them off.
Last year we closely inspected the plants every day when we watered, picked off the worms and minimized damage.
And that's a big advantage of MANUAL watering.  We keep talking about the irrigation system, but I can just see us going to check on the plants and they're GONE because we didn't notice a worm invasion.
We've also caught 7 or 8 mice in the last few weeks in the greenhouse.  Don't know how they get in. And they LOVE those tiny pepper seedlings and salad.
It's definitely a constant struggle and you just have to check all plants every day.
And of course we'll see how effective marigolds, sweet annies, nasturtiums and some of the other plants are at keeping pests away.