It is a well-known fact that many great comedians suffer from depression, and comedy is their way of discharging this emotion and fighting back at this darkness of the soul. It seems that this may be the case for Emily of "I Stand Here Ironing."
In the first allusion to Emily's comedic abilities, Tillie Olsen's narrator, the mother, recalls Emily's pantomimes:
I would be ironing, or preparing food for the next day, or writing V-mail to Bill, or tending the baby. Sometimes, to make me laugh, or out of her despair, she would imitate happenings or types at school.
In the next reference to Emily's comedy the mother calls it "deadly clowning" in its "control, command, and convulsions" that brings "rare and precious laughter" to their lives. Emily's comedy is creative; she invents words--family words --like Shoogily, which means comfort.
That a counselor or psychologist wishes to talk with the mother about Emily suggests that Emily's comedy does, indeed, arise from a troubled soul. The mother tells this person,
She is a child of her age, of depression, of war, of fear--help make it so there is cause for her to know--that she is more than this dress on the ironing board, helpless before the iron.
That's a pretty intersting question, one the story really doesn't explain. I imagine that Emily has develped this "deadly clowning" as a means of coping with the many difficulties she has faced during her lifetime.
Often humor is dark, and I tend to believe such is the case with Emily's humor. Near the end of the story, she decides to skip her finals and flippantly remarks to her mother, "in a couple of years when we'll all be atom-dead they won't matter a bit." The mother sadly thinks that Emily truly believes this comment. Maybe Emily feels that humor is the best way to combat the negative world around her.
Often people will say they laugh to keep from crying; this may be the case with Emily. She uses humor to add levity to a heavy existance. She's been poor, practically abandoned by both parents at various times in her life, chronically ill, and never bonded with her family because of these things. Likely she is very lonely, and humor helps her gain friends and acceptance.
Humor is also her way of feeling normal. She has noted from childhood that people enjoyed her jokes, even when they thought they were her sister's, so using humor and develping her style is her way of gaining acceptance, too, a way of getting the love she probably craved as a "child seldom smiled at."
For a description of Emily and other characters, see the link below. The second link is to a discussion of themes, one of which is a search for identity. These may be helpful in answering your question.