There are also a wide range of mosquito repellant supplies at 100 yen stores like Daiso, such as bracelets and even stickers which have a mosquito repellant in them (citronella, I think!). The stickers are especially handy for anyone who has children, since you can just stick them on a child's t-shirt and not have to worry about spraying them with a repellant solution.
Yes, mosquitoes are a problem in July. I used to buy those plug in liquid mosquito repellent sets but began to question the chemicals used in those things. Since then, our family has shifted to big family sized mosquito nets (available on Amazon). Mosquito nets work perfectly and are eco-friendly (they don't use electricity or harmful chemicals). As for going outdoors in the daytime, I make a homemade spray with a mix of the following essential oils diluted in alcohol: citronella, lemongrass, rosemary, lavender and peppermint. Smells good, and wards off mosquitos and buyo (tiny black flies whose bites itch for months on end).
Hi Shiroi, mosquitos are technically unavoidable when visting Japan especially this upcoming season. Nonetheless, hopefully some of these options may help you get through it with few uncomfortable and restless nights. The readily available ones in the market are mosquito coils, mosquito exterminating mat and insect repellant air freshener. For added protection, you may also buy ahead in your country before leaving for Japan, that way, you get stronger insect repellants to ward off these insects.