In Pygmalion, how does Shaw depict women in general and Eliza in particular in order to create laughter? What are some relevant quotations?

Much of the humor in Pygmalion and other plays by Shaw revolves around undermining traditional gender expectations. Although the women in Shaw's plays often appear conventional on the surface, they routinely prove stronger than the men, leading to paradoxical situations and dialogue. 
In the initial confrontation between Higgins and Liza, we see a clash of class expectations. Much of the humor results from Liza having quite conventional views of propriety, despite being a flower girl, and Higgins being entirely oblivious to conventions, good manners, or other people's needs and feelings. On one hand, Liza becomes someone we laugh at for her ignorance of the middle-class assumptions we share with Higgins and Pickering, but on the other hand, in her plans to better herself through lessons, we see another Liza: one who is shrewd, practical, and brave.
Mrs. Pearce, the housekeeper, and Higgins's mother exemplify a second type of typical female character we find in Shaw's plays: these characters create humor by puncturing the abstract plans or vague impracticalities of the male characters with clear-headed pragmatism. Even when male characters have distinguished positions, these women create comic effects by being the ones really in control, exercising a form of moral authority. 
Eliza's introduction to polite society creates humor in two ways. First, at times she tries to conform to Higgins' instructions literally and utters things that are extremely incongruous, in part because Higgins himself is utterly hopeless at polite conversation. An example of this is her attempt to discuss the weather, where she says:

The shallow depression in the west of these islands is likely to move slowly in an easterly direction. There are no indications of any great change in the barometrical situation.

The humor lies in the degree to which the scientific precision of her speech is inappropriate to the situation. What is also interesting is that part of the humor is its incongruity in the mouth of a young woman; if Higgins had uttered this, it would not have been funny but merely vaguely pedantic, while in the case of Eliza it seems awkward and artificial.
The second way Eliza creates humor is when her background as a flower girl breaks through in a way to which middle-class society has no comfortable response. The following excerpt shows how both the description of a situation from her past and her own unsentimental attitude towards it create humor in contrast with the polite middle-class expectations of the other women at the "at home day":

LIZA [in the same tragic tone] But it's my belief they done the old woman in.
MRS. HIGGINS [puzzled] Done her in?
LIZA. Y-e-e-e-es, Lord love you! Why should she die of influenza? She come through diphtheria right enough the year before. ... They all thought she was dead; but my father he kept ladling gin down her throat til she came to so sudden that she bit the bowl off the spoon.