Looks to me like the language of hyperbole--exaggeration used for effect. Each of the three characters here uses exaggeration to make or emphasize their points. Kate has literally bound her sister Bianca and is venting her spleen on her; Bianca is literally saying anything she thinks might free her:
Bianca: Unbind my hands, I'll pull them off myself.
Yea, all my raiment, to my petticoat;
Or what you will command me will I do,
So well I know my duty to my elders.
This is a plea in hyperbole--she's going to free herself (which she obviously has not been able to do), she'll strip down to her petticoat if that's what it takes (but clearly that would not satisfy Kate's demand), she'll meekly do anything Kate wants (which we know to be an untruth, for Bianca only does what Bianca wants and would certainly not bow to her sister's wishes).
Katherine: Of all thy suitors, here I charge thee, tell
Whom thou lovest best....
Kate's whole demeanor here is hyperbolic, tying her sister up and railing at her. Specifically, she asks about all Bianca's suitors as if there were many, yet she goes on to name only two. When she speaks to her father, she's angry that he may marry off Bianca, the younger sister, before she is wed.
Katherine: I must dance bare-foot on her wedding day
And for your love to her lead apes in hell.
Clearly she's angry that Baptista loves Bianca best. Her exaggerated picture of what she will have to do as the unmarried daughter is outrageous.
Baptista: For shame, thou hilding of a devilish spirit....
This, spoken to Kate, is exaggerated, of course. Then he bemoans his own state (position) in exaggerated terms:
Was ever gentleman thus grieved as I?
How could he possibly think this really is the worst position any man has eve been in? The answer, of course, is that he's using exaggeration for effect. This is a humorous scene in The Taming of the Shrew, primarily because of the hyperbole each of the characters uses.