Suffocate, asphyxiate, stifle, smother, choke, strangle, throttle can all mean to interrupt the normal course of breathing.
Suffocate commonly refers to conditions in which breathing is impossible through lack of available oxygen or through presence of noxious or poisonous gas.
Suffocate also refers to situations in which breathing is impossible because mouth and nose are covered.
Asphyxiate is likely to refer to situations in which death comes through poisonous gases in the air or through lack of sufficient oxygen.
Stifle is appropriately used to refer to situations in which breathing is difficult or impossible through lack of adequate fresh air and, often, presence of heat.
Smother is likely to be used in situations in which the supply of oxygen is inadequate for life; it often suggests a deadening pall of smoke, dust, or impurity in the air.
Smother also refers to situations in which the mouth and nose are covered so that one cannot breathe.
Choke suggests difficulty in breathing through constriction, obstruction, or extreme irritation within the throat.
Strangle also refers to constriction of the throat, obstruction of the windpipe, or irritation, but it is more likely to indicate fatality or quite serious condition.
Throttle usually suggests external compression of the throat done forcefully for the purpose of subduing or overcoming resistance.