A sump pump is used solely to pump out any ground water or storm water that may enter your basement. It may not be used to pump sanatary waste. The configuration you are describing is very common. The sump pit is placed at the base of the outside stairs entering the basement in order to remove any rain or surface water that may come down the stairway before it can get into the house.
Sump pumps are placed in open pits and normally they should not present any odor problems, however in some situations they do keep a minor ammount of water in the bottom of the pit, and that water can stagnate, which might cause a slight odor. If that is the case you can eliminate the odor by periodically pouring a 1/4 cup of laundry bleach in the pit to sanitize it.
Sump pumps MAY NOT be connected to the house drain system. They must disharge outdoors or to an approved storm drain.
There is a variation of the sump pump which is called a sewage ejector pump. The sewage ejector pump is used when it is necessary to install drainage fixtures below the level of the building drain where you cannot acheive gravity flow.
A sewage ejector pump is required to have a fully water tight enclosure with a removable service access cover and it must be vented. The discharge from a sewage ejector must be pumped to a point above the house drain, then connect to the house drain on the top of the pipe by means of a Wye & 1/8th bend or a Combo.
