1998 Toyota Tercel, automatic transmission, with 170000km on it. The smell has never appeared before last year. When I parked it into the garage last winter the smell was only faint. Now when I park it in the garage it is overwhelming. It's so bad it seeps into the house making the whole first floor and basement smell like gasoline. The smell only occurs when parked and engine off, when it is running there is no smell.
I've checked the ground, there are no leaks. I have not overfilled my gas tank, it is at half level.
Help please! And soon!

About the only thing you can do is a close visual inspection of all fuel lines and components.
Do you have any other symptoms? Check engine light? Less mileage than before?
If you think the fuel system leaking, look for stains around fittings and inline connectors. Areas near fuel lines and such may be cleaner than normal.
There is also a powdered trace spray that can be used. Spray the trace in in suspected areas and operate the vehicle only enough to fully charge the fuel system and inspect, inspect, inspect...

If you think it's evaporating, inspect and replace the charcoal canister as necessary. Consider a sniff test at the fuel fill (this should be done early after the car sits).
Good luck and let us know.

The charcoal canister on your vehicle sits under the hood unlike most of today's cars where it's underneath.
My bet a paycheck on this one would be a faulty purging system in the charcoal canister assy.
Be sure you have the OE gas cap on there and not just any off the shelf brand.