I was going to link you to a post on Neem Oil, but the search function is down today. I have it on file, so I'll just post again. I'm not sure I mention it in the article, but cold-pressed Neem Oil also has good antifungal properties.

The info:

Neem Extract as an Insecticidesize>

In India mainly, but also Asia and Africa, grows a tree all plant enthusiasts should be aware of, Azadirachta indica, commonly known as the "neem" tree, and a relative of mahogany. Extracts from the trees seeds contain azadirachtin, a relatively safe and effective naturally occurring organic insecticide. Let me preface the comments following, by reminding you that the terms "naturally occurring and/or organic" do not universally mean safe. Pyrethrums, rotenone, and even the very dangerous nicotine are all organic insecticides that should be handled with great caution. Neem extracts, on the other hand are very safely used in a wide variety of cosmetics, as a topical treatment for minor wounds, as an insecticide in grain storage containers, bins, and bags, and a whole host of other applications. Neem is very safe for use around birds & mammals. I'll limit this discussion to its use as an insecticide.

Neem works in many ways. It is effective both in topical and a systemic applications. It is an anti-feedant, an oviposition deterrent (anti-egg laying), a growth inhibitor, a mating disrupter, and a chemosterilizer. Azadirachtin, a tetranortriterpenoid compound, closely mimics the hormone Edison, which is necessary for reproduction in insects. When present, it takes the place of the real hormone and thus disrupts not only the feeding process, but the metamorphic transition as well, disrupting molting. It interferes with the formation of chitin (insect "skin") and stops pupation in larvae, thus short-circuiting the insect life cycle. It also inhibits flight ability, helping stop insect spread geographically

Tests have shown that azadirachtin is effective in some cases at concentrations as low as 1 ppm, but some producers use alcohol in the extraction of neem oil from plant parts which causes the azadirachtin to be removed from the oil. Some products touting neem oil as an ingredient actually have no measurable amounts of azadiractin. I use what is referred to either as cold pressed or virgin neem oil. You may also occasionally find it referred to as "raw" neem or "crude" neem oil.

Neem oil is most often used in an aqueous (water) suspension as a foliar spray or soil drench. Commonly, it is diluted to about a .5 to 2% solution, but the suggested ratio for use in container plant culture is 1 tsp. per quart of warm water. A drop or two of dish soap (castile or olive oil soap is best) helps keep the oil emulsified. The mixture is then applied as a mist to all leaf and bark surfaces and as a soil drench to the tree's root system. It should not be applied as a foliar spray on hot days or in bright sun as leaf burn may occur. Remember to agitate the container frequently as you apply and do not mix anymore than you will use in one day. Neem breaks down rapidly in water and/ or sunlight.

Some users of insecticides feel the need to observe the instant results of their efforts in order to be convinced of the effectiveness of what they are using. The application of neem derivatives does not provide this immediate gratification. There is virtually no knockdown (instant death) factor associated with its use. Insects ingesting or contacting neem usually take about 3 - 14 days to die. Its greatest benefit; however, is in preventing the occurrence of future generations. It is also interesting to note that in studies it was found that when doses were given, purposefully insufficient to cause death or complete disruption of the metamorphic cycle, up to 30 surviving generations showed virtually no resistance/ immunity to normal lethal doses, so it appears that insects build no Âresistance to azadiractin.

I have been using neem oil for at least 6 years as both a preventative and fixative and have had no insect problems on my container plants. Applications of cold-pressed neem oil are most effective for use on mites, whitefly, aphids, thrips, fungus gnats, caterpillars, beetles, mealy bugs, leaf miners, g-moth, and others. It seems to be fairly specific in attacking insects with piercing or rasping mouth parts. Since these are the pests that feed on plant tissues, they are our main target species. Unless beneficials like spiders, lady beetles, certain wasps, etc., come in direct contact with spray, it does little to diminish their numbers.
Neem oil does have an odor that might be described as similar to that of an old onion, so you may wish to test it first, if you intend to use it indoors. I've found the odor dissipates in a day or two. As always, read and follow label instructions carefully.
Neem oil can be purchased from many net or local sources. My favorite brand is Dyna-Gro, pure, cold-pressed neem oil. If you have trouble locating a source, you can contact me via the forum or directly.

Al Fassezke

Hi Nova..you certainly have a problem. Of all the pests you mentioned, mealy would be my biggest concern. There's a white scale that resembles mealy, (to a degree, to be honest, if you have one of the two, I hope it's white scale, though, white scale mainly attack citrus.)
Since you're dealing with more than one insect, this is what I'd use on my plants, have used as a preventative and insecidicide.
1 capful of Fish Emulsion in about 16oz of room temp water.
2-4 drops of dish soap, (not Dawn)
Ground or liquid citrus/rind
1-2 cloves of Garlic..finely chopped or left to sit overnight in the water.
Shake thoroughly. Spray every part of plant, (stems/leaves/trunk) including plants without insects. (this mix will NOT harm your plants) though I wouldn't/don't spray on African Violets.
Fish Emulsion emits a fishy odor, but they also sell an odor-less type. Sellers on Ebay have it available at decent prices, but if you can buy locally, that'd be better. The sooner you spray, the quicker insects will die.

After spraying, you need to vent the room. Can you open windows to freshen air? Or better yet, set plants outside? If you take plants out in summer, do a thorough cleaning job in plant rooms. Clean windows, corners, any webbing or spilled soil, dead leaves. Shelves should be scrubbed w/soapy water. A little bleach or vinager wouldn't hurt. Don't mix together.
Air room now and before bringing plants in..if you have a fan, run on low/medium speed, directed away from plants.
Some people use insectidal oils, which work similar to Fish Emulusion. Since I've never used oil, I don't know if/how it works, but I use FE, see what it does.
Depending on the number of plants you have, each should be showered, or if outside, hosed off. Shoot those buggers.
For mealy, (if the plant isn't terribly infested) ppl say rubbing alcohol kills, so wipe away using cotton balls or Q-tips. (any plant that has mealy goes in the trash) Mealy is one bug I can't rid.
There are chemical sprays/systemics if chemicals don't bother you. I'm sure they work well, but be careful when handling. Wear gloves and a mask. If you have children/pets, keep them away from plants altogether. Good luck, Toni

Will continued regular use of neem oil clog up the stoma and slow transpiration and in turn slow growth?

I have used it at 2-week intervals (prolly more frequently than that, TBH) on plants with pest problems and never found it to be problematic, nor have I ever read reports of such.

Al