Keep in mind the difference between the author and his fictional creation: despite writing from a first-person point of view, Poe is laughing at the narrator. This is seen in the word "conceive" which the narrator uses to connect to the chosen definition, but Poe uses to also suggest pregnancy and birth (inconceivable for a male). See the descriptions surrounding the word "sufficient" where the narrator seems to be both laboring mother and child being born.
It is impossible to say how first the idea entered my brain; but once conceived, it haunted me day and night.
Whenever it fell upon me, my blood ran cold; and so by degrees—very gradually—I made up my mind to take the life of the old man, and thus rid myself of the eye forever.
You should have seen how wisely I proceeded—with what caution—with what foresight—with what dissimulation I went to work!
And then, when I had made an opening sufficient for my head, I put in a dark lantern, all closed, closed, that no light shone out, and then I thrust in my head.
And this I did for seven long nights—every night just at midnight—but I found the eye always closed; and so it was impossible to do the work; for it was not the old man who vexed me, but his Evil Eye.
The example sentence focuses on describing how the old man would have to be intellectually profound to figure out that the narrator had been looking in on him at night. But "profound" also means "deep and complete"--Poe suggests that it is the old man's profound sleep, and not anything the narrator did, that prevented the discovery.
So you see he would have been a very profound old man, indeed, to suspect that every night, just at twelve, I looked in upon him while he slept.
Never before that night had I felt the extent of my own powers—of my sagacity.
As a verb, "stifle" means "smother or suppress" and "conceal or hide"--the example sentence uses the past tense form of the verb as an adjective to describe the old man's groan. This stifled groan foreshadows the method of murder, the concealment of the body, and the narrator's struggle to suppress his guilt.
It was not a groan of pain or of grief—oh, no!—it was the low stifled sound that arises from the bottom of the soul when overcharged with awe.
Many a night, just at midnight, when all the world slept, it has welled up from my own bosom, deepening, with its dreadful echo, the terrors that distracted me.
Yes, he had been trying to comfort himself with these suppositions: but he had found all in vain.
The word is also used in descriptions of a beating heart: "It was a low, dull, quick sound—-much such a sound as a watch makes when enveloped in cotton." Compare with the note for "stifled"--both foreshadow later actions and emotions. Here, the narrator connects the verb to Death, which he personifies to separate from himself.
All in vain; because Death, in approaching him had stalked with his black shadow before him, and enveloped the victim.
And it was the mournful influence of the unperceived shadow that caused him to feel—although he neither saw nor heard—to feel the presence of my head within the room.
When I had waited a long time, very patiently, without hearing him lie down, I resolved to open a little—a very, very little crevice in the lantern.
So I opened it—you cannot imagine how stealthily, stealthily—until, at length a simple dim ray, like the thread of the spider, shot from out the crevice and fell full upon the vulture eye.
"Hideous" also means "so extremely ugly as to be terrifying"--both definitions fit because the narrator describes the eye's physical features (which he compares to a vulture's) as well as its nature ("Evil Eye" that made his blood run cold).
I saw it with perfect distinctness—all a dull blue, with a hideous veil over it that chilled the very marrow in my bones; but I could see nothing else of the old man's face or person: for I had directed the ray as if by instinct, precisely upon the damned spot.
It increased my fury, as the beating of a drum stimulates the soldier into courage.
Poe is a poet as well as a short story writer. This is suggested by the word "refrain" which also means "a phrase or verse repeated at intervals throughout a song or poem." This poetic device can be seen throughout the story, but is most evident with this example sentence, which uses "refrain" as a verb but also serves as a refrain whose idea and words are repeated in the same paragraph.
But even yet I refrained and kept still.
If still you think me mad, you will think so no longer when I describe the wise precautions I took for the concealment of the body.
The night waned, and I worked hastily, but in silence.
"Cunningly" and "cleverly" are synonyms connected to being smart, often in a dishonorable way. The use of both adverbs seems unnecessary, but it emphasizes the narrator's pride, which he adds to with mentions of his "sagacity" and "wise precautions." The repetitive points about how smart he is are contradicted by almost everything else he describes about his thoughts and actions.
I then replaced the boards so cleverly, so cunningly, that no human eye—not even his—could have detected any thing wrong.
There was nothing to wash out—no stain of any kind—no blood-spot whatever. I had been too wary for that.
There entered three men, who introduced themselves, with perfect suavity, as officers of the police.
In the enthusiasm of my confidence, I brought chairs into the room, and desired them here to rest from their fatigues, while I myself, in the wild audacity of my perfect triumph, placed my own seat upon the very spot beneath which reposed the corpse of the victim.
The first use of the adjective connects to the chosen definition, since at this point, the narrator's head was aching and he thought that was causing the ringing in his ears. By the end of the example sentence, "distinct" also means "constituting a separate entity or part" since the ringing had taken on a life of its own.
The ringing became more distinct:—It continued and became more distinct: I talked more freely to get rid of the feeling: but it continued and gained definiteness—until, at length, I found that the noise was not within my ears.
I talked more quickly—more vehemently; but the noise steadily increased.
I arose and argued about trifles, in a high key and with violent gesticulations; but the noise steadily increased.
They heard!—they suspected!—they knew!—they were making a mockery of my horror!
Anything was more tolerable than this derision!
I could bear those hypocritical smiles no longer!
Compare this verb with the noun "dissimulation"--both connect to deception, but the moods around each word are opposite: the narrator is proud of his own dissimulation, but he cannot handle what he assumes to be the dissemblance of the police (which is actually the projection of his own deception onto others). This and the confession (here and in the entire story) might suggest that the narrator, although insanely murderous, has an essentially honest nature.
I shrieked, "dissemble no more! I admit the deed!—tear up the planks! here, here!—It is the beating of his hideous heart!"