Each of your sinks should have a trap installed underneath, a U shaped bend in the pipe (a trap) designed to hold some water and keep gases from coming out of the waste system. The pipes in the walls must be properly vented to prevent this water from being sucked out of the trap each time you empty the sink. It sounds like either your vent lines were not properly installed or have been blocked since.

There should be at least one 3-4 pipe sticking up through your roof. You may want to check to see that it is not covered over. Other than that, you need to get a plumber to check the situation. If you had this house built or purchased it new, call your builder asap, as you should still be under warranty. You may also want to call your local code enforcement agency, as they should not have approved if there were vent issues. If you bought an older house, you are on your own but you should call a qualified plumber.

Until you can get a plumber there, you can reduce or eliminate the smell by running the water a bit after you drain the sink each time. Let it drain completely, then run the water for 5 seconds or so. This should be enough to fill the trap and stop the gas.