"Ladyface" has a good point, dry P-traps or non-existent P-traps can allow sewer gas to flow from the sewage system and back into the house, but after some use of all of the drains a dry trap would contain water and thus work properly. The age of the house would certainly indicate that there should be P-traps on every drain unless the house was built out of code.
My best guess would be that your main drain line is clogged causing the backup that you talked about. Whether on a septic tank or municipal sewer system, your main drain can become clogged with tree roots or a build up of debris from over the years and an unblocker will not clear it an auger must be used. You will either need to rent an auger and clean your drain or hire a "rooter" company to clear the obstruction. Additionally if you are on a septic system and the tank is full the same backups would occur. In case of the latter, as soon as you send any major amount of water down the drain to the septic tank the methane gas, which accumulates at the top, has no where to go but back up the pipes and into the house through any drain that is missing a trap, or pipe that may have minor cracks.
Because you say that the smell is coming from the kitchen sink I would check the p-trap there to see if it is holding water, look for long term leak evidence under the sink where the trap may have rusted out allowing water to leak out of the P-trap and leave it dry and allowing the methane gas to come back up the line.
I hope this helps, write back and let me know how you do.