Run the dryer (on cold, to save $$) and see if you can pin down the fixture(s) the gas is coming from. The dryer pumps a lot of air outside, and that air has to be replaced from somewhere. In your case it appears to be replaced by sucking gas out of the sewer, which may be the easiest makeup air to find if your (new!) house is really tight. Opening a window near the dryer is the easiest way to fix this, as you've found.
Unfortunately, this doesn't explain the smell when you're taking a shower, but you're not alone. There's a really interesting thread on this forum describing a similar problem, with no solution found yet.