Here is a simple version of the effects of sewer gas:
Indoor Air -- Sewer Gas
You can do a google search for "msds hydrogen sulfide" and "msds methane" for specific info.
A "P trap" , "s trap" or "j trap" is nothing but a u shaped section of pipe which prevents sewer gas from escaping into the home.
Your toilet has one built into the toilet and that "U" thing in the drains for your sinks etc, hold a bit of water.
Unused showers or sinks can cause the water to evaporate. Pouring 4 cups of vegtable oil down an unused drain will not evaporate.
Can you take a picture of the vent stacks on the roof that might serve the second floor? You can post using "go advanced/manage attachments". There's a possibility they aren't high enough or have other problems.
If the vent is clogged, it can be fixed by running a snake from the roof.
If any of your fixtures gurgle, this is a sign of a plugged vent.
It's odd that you said sink, tub and sinks. If indeed it's all of those fixtures, then the vent is suspect.
If it's one, then it could be no trap or non-use.
Now it is possible that the wind could be forcing things down the stack too. That can be fixed as well.
Because you added "wind", I suspect another issue, so I'd like to see the layout of the pipes on the roof relative to any overhangs, etc.
If it really is wind, you can install AAV's with the proper cap on the roof vent.
e.g.
http://www.plumbingsupply.com/autovent.html
This will prevent wind from pushing bad gas into the house.