Speech and Dialogue
In Titus Andronicus language use is an indicator of how much power a character has. Take Lavinia, for example. At the beginning of the play, she is completely silent when Bassianus and Saturninus fight over who will marry her (and nobody bothers asking her what she wants). This suggests that Lavinia is an object of desire, not a figure whose desires are relevant to those around her. Later Lavinia is brutally silenced when her rapists, Demetrius and Chiron, cut out her tongue. (This is also why it's so fitting that Titus orders that Demetrius and Chiron be gagged just before he bakes them into a pie: "[...] bind them sure, / And stop their mouths, if they begin to cry" (5.2.17). After Aaron confesses to being the mastermind behind all of Titus's suffering, Lucius orders him bound and gagged as well: "Sirs, stop his mouth, and let him speak no more" (5.1.14). Up to this point, Aaron has been in almost total control, but here he can no longer "torment [the Andronici] with [his] bitter tongue"(5.1.12).
Sex and Love
A character's sex life can tell us a lot about his or her character in this play. Tamora's sexuality is meant to align her with viciousness, cruelty, and immorality. When Saturninus says he's thinking about making Tamora his empress, she responds by promising to be a "handmaid to [his] desires." Tamora doesn't really care about Saturninus, but she promises to keep him very satisfied in exchange for power, which suggests that she is willing to do just about anything for the kind of power that will enable her to get back at the Andronicus family. This includes encouraging her sons to rape Lavinia while she's off rolling around in the forest with Aaron. Did we mention that Tamora's secret affair with Aaron continues even after she's married to Saturninus?
Lavinia, on the other hand, is chaste and virtuous, which signals her innocence. (In Shakespeare's day, being "chaste" meant that a woman was a virgin when she got married, and after her wedding night she was completely faithful to her husband.) In fact, the play goes out of its way to demonstrate that, even after Lavinia is raped, she remains virtuous. When Marcus finds Lavinia after she's been assaulted, she turns away in "shame" when he guesses that she was raped. She also blushes (despite the fact that she's lost a lot of blood):
Ah, now thou turn'st away thy face for shame!
And, notwithstanding all this loss of blood,
As from a conduit with three issuing spouts,
Yet do thy cheeks look red as Titan's face
Blushing to be encountered with a cloud. (2.4.1)
Compare Lavinia's extraordinary ability to blush with Aaron's refusal (or inability?) to blush when his adulterous affair with Tamora is discovered: "Fie, treacherous hue, that will betray with blushing / The close enacts and counsels of the heart!" (4.2.18).
Social Status (Race and Nationality)
Early on in Titus Andronicus, we're led to believe that Goths and Moors are "barbarous" and the Romans are civilized. Marcus enters the stage and declares that Titus has been at war with the "barbarous Goths" (1.1.1), who are soon paraded through town like captive animals. Later, Bassianus accuses Aaron of being a "barbarous Moor" (2.3.2). But Shakespeare soon makes it clear that there's not much difference between the Romans, Goths, and "Moors." Just about everyone in this play participates in the destructive cycle of violence and revenge. Titus sacrifices Tamora's eldest child (1.1), Aaron and Tamora encourage Demetrius and Chiron to rape Lavinia (2.3), and so on. For more on this topic, see "Themes: Race."