I have a property that is suddenly having an offensive odor in the kitchen area.

No one lives there so first thing I did is to open all the faucets, shower, flushed toilets to make sure the trap seals are not open.

The odor remains. Seems to happen right after a recent heavy rain storm. There are gas appliances in the house.

So is there a way to tell the difference between sewer gas, natural gas leak, and some dead animal rotting? They kind of smell the same?

Sounds like it could be a dead mouse or rat

In Virginia we have heavy clay soil, and sometimes just when it’s wet, a nasty odor arises right from the ground!! Luckily not everywhere

You said the smell "Seems to happen right after a recent heavy rain storm." Is there any dampness inside the house? Are there weeping tiles or a french drain inside or outside the foundation? Is there a sump pump in the basement? Is there a drain tied to a sewer line, or to the street gutters?

If it is a dead animal, the smell usually fades after a week or two.

If you have a bad sense of smell, bring in someone with a good nose. The smell of natural gas and sewer gas is quite different if you have a good nose.