Re mosquitos - first thing you want to do is find out if they're breeding inside the house. They like standing water - check the basement. Unused toilet tanks and drain traps in an unlived-in-for-a-while house quailfy as standing water, but as long as you're running water in them now, there shouldn't be anything new hatching.

If they're coming in from outside, check your screens both for holes and to make sure they're firmly seated in the windows.

As for the mosquitos already in the house, how many?
Only a few, but too many: squish

Ravening hordes:
-Many biting mosquitos are attracted to light
-ALL are attracted to carbon dioxide. You can't stop exhaling, but it's a handy-to-know fact. The mosquitos will go where the highest concentration of CO₂ is. Dry ice is frozen carbon dioxide.

• The traps we used in the Air Force consisted of dry ice in a paper bag, hung up (because the evaporating CO₂ goes down)
  with a tube rubber-banded to the bag's opening going down to the mouth of the trap. You could probably just set the bag & dry ice so the opening's right in front of the fan.
  
• The trap itself - well I can't remember exactly. Reconstructed for home use. The basics would include a little teeny, weak fan (one of those personal desk fans or weaker) blowing into the mouth of a mosquito-proof net.
  
• We used to use cut off bits of "No-Pest Strips" in a jar to kill them, but you could just stick the whole net in a plastic bag and shove it in the freezer for a few hours. Shake the skeeters out and start again.

Paper bags, nets and fans are easy. The hardest part is finding dry ice. Medical laboratories will either have it or know where to get it.

If the mosquitos aren't sounding as annoying as all this, go back to squishing. You'll eventually wipe out the current crop and hopefully prevent re-infestation.

In any case, I sympathize with you. When I moved in here, I found I'd have to put up with various plagues.
Moths: The dry food is in plastic zip-lock bags, sealable plasticware or the fridge/freezer.
Squirrels: Fix the hole in the roof. Catch the one that got in through the unused wood stove chimney and plug that up.
Ants: Ant cups
Spiders: If I can't see them, I don't care. If I can catch them, they go outside. If I can't, they get squished.
Flies: Just wait for fall when the cluster flies start looking for a winter home. Fly stips. Gross, but effective.
Chipmunks in the basement: Yell at them and chase them around. They're smarter than squirrels. (If mine have been back, they've been quiet.)
Mice: Don't leave anything they can eat lying around. Reducing clutter helps (I've got a snowball's chance in you-know-where to do THAT one). Mouse traps. Cat.
I know I'm forgetting something...

Sorry for the length, but good luck.