I have an odd problem in an old house I just bought. The big problem is that just after doing laundry, and only then, there is a strong sewage smell. The second, and probably connected problem, is that when the washer drains, there is a backup in the sink next to the laundry room. My guess is that the design of the pipes is bad and that the washer water knocks the water out of the P trap of the sink, letting the gas seep back up the drain line. The smell only lasts a few minutes but is strong. There is no access to the pipes, but I've been told two things. ONe to add a t to the drain pipe of the washer and have it vent 9 inches above where the hose enters the pipe, which will help with flow and prevent the sink back up. And someone else told me that when they added the washer drain into the line, they must have had it coming into the main line at the same point as the sink drain pipe and that if it's reconfigured to enter the line either above or below where the sink drain enters, the problem of backing up would be solved. That does make sense. Is it possible that the backing problem is also causing he gas smell?

It sounds like this drain is unvented or the vent is clogged. Also the drain line is too small or also clogged. What size is the drain pipe your washer empties into? You need a minimum of 2" preferably a 3" drain line. You may be able to get away with adding a air admittance valve (AAV) on top of that new 9" pipe but do not allow it to be open to the room, you'll get more gas than ever.