These are always tough to fix and to find. The smell could be coming from one of a multitude of problems.
First and foremost is the venting problems. When a vent is clogged (from ice or birds nests), it prevents upstairs toilets from relieving the air pressure that builds up when you try to put 1.5 gallons of water into a pipe filled with air. It tries to push the air ahead of it, but with the vent clogged, it pushes it out the vents on the toilets in the basement or other fixtures. Since water weighs 8.33 pounds per gallon, it puts a pressure on the piping to offset that weight. Most traps have a water depth seal of 2 inches, which equates to 3 tenths of a pound. The air inside the pipe ahead of the water takes the path of least resistance, often right through the traps below the line, since all vents are interconnected, even the vent for the basement bathroom.
Another problem is a clogged main line, when the water flows down the main, if its partially clogged, the air ahead of the water can not escape fast enough. Even though the water may seem like its draining, because there is alot of piping it can fill below the toilet and in the horizontal line. The air knows instantly there is no place for it to go, so it again tries to come out other traps.
Finally, your sewage ejector lid can be unsealed. If there are openings or the lid is not calked to the sump basket, the sewer gas can come out everytime any fixture runs.