In one of the earlier episodes the Professor is going to be taken away by the Reapers to go to a retirement community in space at the age of 150(?). And from one of the movies we learn that the youngest of Mom's sons is her love child with the Professor. How old are Mom's children and how old is Mom?
Their exact ages are never given. The best estimates are as follows:
Mom: born sometime before 2881, when the Professor began working for her company.
Her sons (Walt, Larry, and Igner): Based on the movie Bender's Game, they would appear to be in their thirties, with Walt and Larry being slightly older than Igner since they were around when Professor Farnsworth fathered him around the time he discovered dark matter.