Dryer Sheets, Bananas, and Mosquitos

The state bird in my state is the mosquito (or at least it seems like it is). We can't even go outside right now without being swarmed and attacked. The other day I got 5 bites just going from my front door to my car, and these are not ordinary bites either- some are as big as a nickel! I feel trapped in my house by these little vile vermin and don't know how to protect myself and my family from the little vampires. Are we or are we not a more intelligent species?! We, the human race, who have pushed into extinction so many species on the planet are being trapped inside by a little bug! There's got to be something we can do- someone out there who has spent their life in an endless battle with mosquitoes and knows how to help us kill in greater numbers.

Here is what I've tried when it comes to keeping the bugs off of me:
Dryer Sheets- I've been told that if you keep a dryer sheet in your clothes then the buggers will stay away... hmm... well, I don't know how well it worked since there will still a lot of mosquitoes flying around. If it reduces the number from 5,000 to 2,500 then I don't know how well that really helped.
Bug Spray/Repellent- I hate spraying on noxious chemicals all over my body, I hate the feel of it, and I hate the smell of it. With all the pain it takes to use this stuff- it does seem to help. After a whole can, the bugs around me went from giant swarm to mild nuisance.
Bananas- I've also been told that if I eat bananas then mosquitoes won't find my blood so enticing. I don't know if this has helped either since I still have 12 bites on me right now.

Here is what I've tried when it comes to relieving the horrible pain of the bites:
Banana Peels- I was also told that if you rub a banana peel on your bite then it will help the itch and pain. It felt really good while I was applying it, but didn't help in the least with the pain and itch afterward.
Itch Ointment- I put this on ever bite I had and they still became more swollen the next day and the itch was very very mildly diminished.
Hand Sanitizer with Alcohol- This supposedly kills the parts of the bites that have the poison in them and relieves the itch. It helped slightly, but I had to keep putting it on over and over.

What have you tried that has worked or hasn't worked? Is there some random Grandmother's remedy that will cure my itch or keep the little buggers off of me and my family? What products do you like and use and what should I try? I've gotten to the point where natural remedy or chemical overload will have to do- I'm so sick of being a prisoner in my own house. Help me!