A monologue refers to a speech by one person in a drama. It is usually meant to be heard or entertained by/toward a specific listener. I might consider Juliet's monologue after she finds out that her Romeo had murdered Tybalt,
"Shall I speak ill of him that is my husband?
Ah, poor my lord, what tongue shall smooth thy name
When I, thy three-hours wife, have mangled it?....." (Act 3 scene 2)
Soliloquy is of course an extended speech when other characters have left the stage. We usually get some inner thoughts of the character.Here Romeo is going on about his latest obsession and muse.
"But soft! What light through yonder window breaks?
It is the east, and Juliet is the sun.
Arise, fair sun, and kill the envious moon,
Who is already sick and pale with grief... (Act 2 scene 1)
Dramatic Irony is when the audience knows something that a character doesn't. Consider when Romeo thinks Juliet is dead inside her tomb instead of merely sleeping in Act 5 scene 3.