What imagery and dramatic irony is present in Juliet's lines (1-33) of Act 3, Scene 2 in Romeo and Juliet?

Juliet has an impatient yet pensive tone as she borrows from mythological imagery in the lines you mention.  In this lesser-known monologue by Juliet, she waits for her new husband to come to her and consummate the marriage.  Quite obviously, Juliet is impatient.  She has to wait for night to fall, and it simply can't come fast enough.  All of Juliet's images in her monologue revolve around this one theme.  Most interestingly, however, Juliet borrows from Greek mythology to set the scene:

Gallop apace, you fiery-footed steeds, / Towards Phoebus' lodging!  Such a wagoner / As Phaeton would whip you to the West / And bring in cloudy night immediately.  (3.2.1-4)

What an interesting image to use, one that definitely has been given by an impassioned lover!  Phaeton, of course, couldn't control the horses.  Therefore, although, night might come faster, it certainly wouldn't come with any regularity or certainty.  All of Juliet's other images here revert back to this image of night coming quickly.  Juliet even uses apostrophe when she directly addresses night in her monologue.  Juliet combines apostrophe with metaphor in a beautiful image describing her lover:

Come, gentle night; come, loving, black-browed  night; / Give me my Romeo; and, when he shall die, / Take him and cut him out in little stars, / And he will make the face of heaven so fine / That all the world will be in love with night / And pay no worship to the garish sun.  (3.2.20-25)

Oh, but the dramatic irony in this scene is enough to break anyone's heart!  The audience knows that Romeo has killed Juliet's cousin, Tybalt.  This murder will most certainly foul the lovers' chances to be together!  Juliet, of course, has no knowledge of this until the Nurse tells her later in the scene.  The audience, then, has no choice but to look on with sad eyes.

How does Juliet's soliloquy in lines 33–44 exemplify dramatic irony?

Presumably you are speaking of Juliet's soliloquy in act 2, scene 1. Juliet has other soliloquies that encompass those line numbers, but which don't show dramatic irony.

Dramatic irony occurs when the audience knows something a character in a play does not. In this case, Juliet is on her bedroom's balcony, speaking aloud. We as an audience know that Romeo is hidden in the shrubbery listening, which Juliet does not know. We also know that Romeo is as deeply in love with Juliet as she is with him.

Juliet reveals her love for Romeo in this soliloquy, not knowing she is speaking to him. She says,

Deny thy father and refuse thy name.

Or, if thou wilt not, be but sworn my love,

And I’ll no longer be a Capulet.

Being confident of Juliet's love helps embolden Romeo to confess his own love strongly (if he needs any help). Juliet's soliloquy speeds along the action of the play by bringing the lovers all the more quickly to an understanding that will lead them to marry the next day.

How does Juliet's soliloquy in lines 33–44 exemplify dramatic irony?

Dramatic irony is when something happens that only one or a few characters on stage and the audience know about...all other characters are in the dark.  In this soliloquy, Juliet is grieving that she is in love with Romeo, and he is a member of her family's arch enemy family.  She is speaking on her balcony about how she loves him and how if he were any other name (from any other family) it would all be OK.  She doesn't know it, but Romeo is in the bushes below listening to her every word. The audience knows this, too.  Viola!  Dramatic irony.