First, mood and tone aren't the same thing. It's common that teachers lump those two items together because they do come hand in hand quite often. Additionally, tone will often affect mood, so many readers assume that they are equivalent.
In a nutshell, tone is more about the author or speaker of a piece, and mood is more about the reader. Tone refers to an author's or speaker's use of words and writing style to convey his or her attitude toward a topic. Tone could be defined as how/what the author feels about their subject. What the reader feels is known as the mood.
I'll start with tone for this poem. When the poem starts out, I feel that the speaker's tone is a mixture of solemn, nostalgic, and perhaps even distracted. The poem begins late at night with the speaker trying to find some way to take his mind off the lost Lenore. He's very sad about losing his loved one, and he can't stop thinking about her.
Eagerly I wished the morrow;—vainly I had sought to borrow
From my books surcease of sorrow—sorrow for the lost Lenore—
For the rare and radiant maiden whom the angels name Lenore—
Nameless here for evermore.
From there, I would say that the tone changes to curious. A strange knocking arrives at his door, but there is nothing there.
That I scarce was sure I heard you”—here I opened wide the door;—
Darkness there and nothing more.
Next, a strange talking bird comes in. At first, the narrator sees the situation as quite curious.
Much I marvelled this ungainly fowl to hear discourse so plainly,
Eventually though, the narrator's curiosity turns toward annoyance and anger at the bird.
“Be that word our sign of parting, bird or fiend!” I shrieked, upstarting—
“Get thee back into the tempest and the Night’s Plutonian shore!
Leave no black plume as a token of that lie thy soul hath spoken!
Leave my loneliness unbroken!—quit the bust above my door!
Take thy beak from out my heart, and take thy form from off my door!”
Finally, the narrator's tone is one of resignation. He knows that Lenore is dead, and he knows that he will never be able to be with her and be happy again.
And my soul from out that shadow that lies floating on the floor
Shall be lifted—nevermore!
As for mood, I would have to say that the mood of the piece is mysterious, melancholic, and a bit morose. The mysterious mood is easily taken care of through the talking raven. That's just weird. As for melancholic and morose, that mood pervades the piece because the narrator is spiraling through depression at the loss of Lenore. The raven doesn't help his depression either. In fact, the raven makes it worse and turns his depression into anger—which leaves him morose.