Perhaps the best way to "strike up" a conversation between Maggie (from Everyday Use) and Walter (from A Raisin in the Sun) would be taking something which they have in common and building upon it.
Both Maggie and Walter live at home. Both have been unable to move out of their mother's home and must come to terms with both this and the fact that they are treated like children.
Therefore, a conversation between the two could focus upon how they feel living at home, how they feel they are treated because of this fact, and the similarities between their lives based upon the previous two facts.
In the end, the conversation could revolve around how they each were able to change their lives (what they did, how they did it, and how they grew during the process).