Google "lemon eucalyptus" insect (including those quotes) and you'll be able to read about studies that show this oil is most effective as a mosquito repellent.
There is currently only one brand available in the U.S. that's using this oil as its active ingredient-- it's called Repel. I searched high and low for it this spring for my daughter, who attracts mosquitos like mad and then gets horrid red welts for weeks afterwards. She scratches them (even in her sleep), they bleed and don't get well, she gets more every time she goes outside... it's an ugly scene.
I bought the oil at the health food store (Aura Cacia, fairly poor quality brand but possibly okay for this purpose) and have been hunting to find a recipe to create a spray with it. Finally found one here.
Homemade All-Natural Mosquito Repellent
1 ounce jojoba oil
3 ounces vodka - Any type of vodka will do, but higher proof vodkas tend to work better.
1 teaspoon lemon eucalyptus essential oil
1 4-ounce spray bottle
Simply add the vodka and oils to the spray bottle. Make sure to shake the bottle well before using as the contents will settle.
Directions for Use
Spray on liberally before going outside. Reapply every 1-2 hours. Just as with commercial products, this mixture should not be ingested.
The author said it needs to be reapplied every 1-2 hours. Since we don't often stay outside much longer than that in the summer, that'll do just fine. No bugs, no toxic chemicals on my babies! (Always test for irritation on the forearm before rubbing an essential oil concoction all over you or your kids-- you know that, right?)