Here are results of some of the field studies that were done on the natural mosquito repelling action of neem oil:
In 1994 the the Malaria Research Centre of Delhi, India, tested whether kerosene lamps with 1% neem oil can protect people from mosquito bites. For that test they burned the lamps in living rooms, and from 6 pm to 6 am caught the mosquitoes sitting on the walls and those attracted to human bait (i.e. volunteers).
Neem oil clearly reduced the number of bites on the volunteers and also the number of mosquitoes caught. The protection was greater against anopheles species (the ones that transmit malaria) than against culex.
A 1995 study at a field station the Malaria Research Centre in Ranipur, Hardwar, India, tested a mix of 2% neem oil mixed in coconut oil.
They showed that applying that mixture to the skin provided significant protection from various mosquitoes. It worked best against anophelines, offering 96-100% protection! (The malaria transmitting anopheles mosquitoes fall into this group). The numbers for other species were 85% for Aedes (carries dengue fever), 61-94% for Culex spp. (can carry West Nile virus) and 35% for Armigeres.
In 1996 the Malaria Research Centre of Delhi, India did another field trial with kerosene lamps in an Indian village. Kerosene lamps with 1% neem oil were kept burning from dusk to dawn in living rooms.
They found that the lamps kept the mosquitoes out of the living rooms and that the malaria incidents of the population dropped dramatically (from about ten cases per thousand people to only one in thousand). Once the lamps were removed, the mosquitoes returned and so did the malaria.
(As for the safety of this method, another 1996 study by the Malaria Research Centre in Delhi, India tested the effects of kerosene lamps with 1% neem oil. Clinical examination of 156 adults and 110 children did not reveal any major adverse effects after one year of exposure to 1% neem oil.)
It shows that depending upon what species of mosquito you are dealing with, effectiveness of use varries.
For malaria protection neem oil is fantastic.
If you combine the 96-100% protection rate of the home made mosquito repellent with burning some neem oil when sitting outside and wearing sensible clothing, you are well protected indeed.
But take for example the common house mosquitoes in northern America. They are a culex species, and neem's effectiveness against culex varies. The number of bites will be greatly reduced, but you probably still get bitten.
There are options of mixing Neem oil with other ingredients to increase the effectiveness against culex.
So to make an educated guess how effective neem oil will be, it helps to know what mosquito species are common in your area or in the area you want to visit.
There are many different kinds of mosquitoes and they are specific to different regions.