I have a septic tank that was placed in my yard. The yard is mostly clay and there is no leach bed. To prevent the sewer from backing up through the tank lid and into the yard the overflow pipe that usually drains into a leach bed was routed to a pipe that goes under a road and drains into a wooded area. Since doing this I am getting a very bad sewer gas smell in my house. The pipe it connects into is a 6 inch iron pipe that goes to my house basement where a 3 inch pipe goes into it that drains my basement water (shower, washing machine). There are several traps in the 3 inch pipe. The more water I use that goes into the septic tank the worse the smell gets until we have to leave the house. It does not matter how much water I put through the basement pipe I still get the smell. The house is a duplex and my inlaws live on the other side and they get the smell also. I am at wits end trying to eliminate this smell with no problems. If the pipe is disconnected the smell goes away but my yard turns into a sewer swamp.

What you discribed has several flaws all of which could be causing your issues. Proper septic design requires that NO water comes to the surface at all. This means both black water and gray water. What disturbs me is that the overflow as your call it is allowed to drain into an another persons property i.e. woods.
This tells me right off that the entire system has been installed incorrectly.
I assume that the basement drainage system is pumped up to the tank. If there is no pump the top of the septic system would have to be at least a foot below the surface of the floor in the basement. Otherwise any water that enters into the drain would not be able to drain into the tank as it began to fill. When this happens the waste would not drain out even past the traps and odors would begin to develop.
Now you also said that there are several traps in the three inch pipe? Only one trap at each fixture with proper vent is supposed to be installed. You can have a main trap on the six inch pipe but that as well must be vented to the outside of the home. If you have no vents and assuming the water is properly draining by pitch of the pipe the water as it drains would draw the water out of the traps rendering them useless.
I would strongly suggest that you pay for a profesional evauation of your current system by another company other then the one that did the install of your current system. As there is just to many things that based on your discription do not sound right. I know in the NJ area septic systems can cost $20,000 and up if a pump leach field system is required.